Kinetic Energy

k www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk k www.studyguide.pk www.studyguide.pk www.studyguide. k www.studyguide.pk www.studyguide.pk www.studyguide.
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A sphere has volume V and is made of metal of density ρ.
(a) Write down an expression for the mass m of the sphere in terms of V www.studyguide. k www.studyguide.pk www.studyguide.pk and ρ.
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k www.studyguide.pk www.studyguide.pk www.studyguide.
(b) The sphere is immersed in a liquid. Explain the apparent loss in the weight of the sphere. k www.studyguide.pk www.studyguide.pk www.studyguide.
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k www.studyguide.pk www.studyguide.pk www.studyguide.
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.......................................................................................................................................... k www.studyguide.pk www.studyguide.pk www.studyguide.
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k www.studyguide.pk www.studyguide.pk www.studyguide.
(c) The sphere in (b) has mass 2.0 x 10 kg. When the sphere is released, it eventually falls in the liquid with a constant speed of 6.0 cm s . k www.studyguide.pk www.studyguide.pk www.studyguide.
(i) For this sphere travelling at constant speed, calculate k www.studyguide.pk www.studyguide.pk www.studyguide.
1. its kinetic energy, k www.studyguide.pk www.studyguide.pk www.studyguide. k www.studyguide.pk www.studyguide.pk www.studyguide. k www.studyguide.pk www.studyguide.pk www.studyguide. k www.studyguide.pk www.studyguide.pk www.studyguide. kinetic energy = ...................................... J k www.studyguide.pk www.studyguide.pk www.studyguide.
2. its rate of loss of gravitational potential energy. k www.studyguide.pk www.studyguide.pk www.studyguide. k www.studyguide.pk www.studyguide.pk www.studyguide. k www.studyguide.pk www.studyguide.pk www.studyguide. k www.studyguide.pk www.studyguide.pk www.studyguide. rate = ...................................... J s
[5]
k www.studyguide.pk www.studyguide.pk www.studyguide.
(ii) Suggest why it is possible for the sphere to have constant kinetic energy whilst k www.studyguide.pk www.studyguide.pk www.studyguide. losing potential energy at a steady rate.
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k www.studyguide.pk www.studyguide.pk www.studyguide.
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www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk held 1.6 m above a horizontal steel plate, as illustrated in Fig. 4.1.
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A steel ball of mass 73 g is www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. steel ball mass 73 g www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.
1.6 m www.studyguide.pk www.studyguide.pk www.studyguide. h www.studyguide.pk www.studyguide.pk www.studyguide. steel plate www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.
Fig. 4.1
The ball is dropped from rest and it bounces on the plate, reaching a height h. www.studyguide.pk www.studyguide.pk www.studyguide.
(a) Calculate the speed of the ball as it reaches the plate. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. speed = .......................................... m s
[2]
www.studyguide.pk www.studyguide.pk www.studyguide.
(b) As the ball loses contact with the plate after bouncing, the kinetic energy of the ball is www.studyguide.pk www.studyguide.pk www.studyguide.
90% of that just before bouncing. Calculate
(i) the height h to which the ball bounces, www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. h = ............................................... m www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.
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www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pkball as it leaves the plate after bouncing. www.studyguide.
(ii) the speed of the www.studyguide.pk www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. speed = .......................................... m s
[4]
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(c) Using your answers to (a) and (b), determine the change in momentum of the ball during the bounce. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. change = ............................................. N s [3] www.studyguide.pk www.studyguide.pk www.studyguide.
(d) With reference to the law of conservation of momentum, comment on your answer to (c). www.studyguide.pk www.studyguide.pk www.studyguide.
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www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pka cylinder by means of a moveable piston, as illustrated in Fig. 5.1.
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Some gas is contained in www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. gas www.studyguide.pk www.studyguide.pk www.studyguide. moveable piston www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. cylinder www.studyguide.pk www.studyguide.pk www.studyguide.
Fig. 5.1
State how, for this mass of www.studyguide.pk www.studyguide.pk gas, the following changes may be achieved.www.studyguide.
(a) increase its gravitational potential energy www.studyguide.pk www.studyguide.pk www.studyguide.
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www.studyguide.pk www.studyguide.pk www.studyguide.
(b) decrease its internal energy www.studyguide.pk www.studyguide.pk www.studyguide.
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(c) increase its elastic potential energy www.studyguide.pk www.studyguide.pk www.studyguide.
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www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.
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www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pka www.studyguide.pkvariation with time t of
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A ball falls from rest onto flat horizontal surface. Fig. 3.1 shows the www.studyguide. the velocity v of the ball as it approaches and rebounds from the surface. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.
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v/ms www.studyguide.pk www.studyguide.pk www.studyguide.
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3 www.studyguide.pk www.studyguide.pk www.studyguide.
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www.studyguide.pk www.studyguide.pk www.studyguide.
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0
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t/s www.studyguide.pk www.studyguide.pk www.studyguide.
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www.studyguide.pk www.studyguide.pk www.studyguide.
-3
-4 www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.
Fig. 3.1
Use data from Fig. 3.1 to determine www.studyguide.pk www.studyguide.pk www.studyguide.
(a) the distance travelled by the ball during the first 0.40 s, www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. distance = ……………………………………. m [2] www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.
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www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.
(b) the change in momentum of the ball, of mass 45 g, during contact of the ball with the surface, www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. change = ………………………………….. N s [4]
(c) the average force acting on the ball during contact with the surface. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. force = ……………………………………. N [2] www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.
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www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pktowww.studyguide.pk car as it moves down
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A student has been asked determine the linear acceleration of a toy www.studyguide. a slope. He sets up the apparatus as shown in Fig. 3.1. www.studyguide.pk www.studyguide.pk www.studyguide. d www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.
Fig. 3.1 www.studyguide.pk www.studyguide.pkvalues of d. A graph of www.studyguide. The time t to move from rest through a distance d is found for different d (y-axis) is plotted against (x-axis) as shown in Fig. 3.2. www.studyguide.pk twww.studyguide.pk www.studyguide.
120
www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.
100
www.studyguide.pk www.studyguide.pk www.studyguide. d / cm www.studyguide.pk www.studyguide.pk www.studyguide.
80
www.studyguide.pk www.studyguide.pk www.studyguide.
60
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40
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0
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t /s www.studyguide.pk www.studyguide.pk www.studyguide.
Fig. 3.2 www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.
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www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pkthe graph is a straight line through the origin.www.studyguide.
(a) Theory suggests that www.studyguide.pk
Name the feature on Fig. 3.2 that indicates the presence of www.studyguide.pk www.studyguide.pk www.studyguide.
(i) random error, www.studyguide.pk www.studyguide.pk www.studyguide.
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(ii) systematic error. www.studyguide.pk www.studyguide.pk www.studyguide.
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www.studyguide.pk www.studyguide.pk www.studyguide.
[2]
(b) (i) Determine the gradient of the line of the graph in Fig. 3.2. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. gradient = ........................................... [2] www.studyguide.pk to (i) to calculate the acceleration of the toy down the slope. www.studyguide.pk www.studyguide.
(ii) Use your answer
Explain your working. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. acceleration = ........................................ m s [3] www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.
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www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.
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A ball has mass m. It is dropped onto a horizontal plate as shown in Fig. 4.1. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. plate v www.studyguide.pk www.studyguide.pk www.studyguide.
Fig. 4.1 www.studyguide.pk www.studyguide.pk www.studyguide.
Just as the ball makes contact with the plate, it has velocity v, momentum p and kinetic www.studyguide.pk www.studyguide.pk www.studyguide. energy E .
(a) (i) Write down an expression for momentum p in terms of m and www.studyguide. www.studyguide.pk www.studyguide.pk v.
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www.studyguide.pk www.studyguide.pk www.studyguide.
(ii) Hence show that the kinetic energy is given by the expression www.studyguide.pk www.studyguide.pk www.studyguide. p .
E =
2m
www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.
[3]
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www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk 4.5 m s . It bounces www.studyguide. (b) Just before impact with the plate, the ball of mass 35 g has speed from the plate so that its speed immediately after losing contact with the plate is
3.5 m s . The ball is contact with the plate for 0.14 s. www.studyguide.pkin www.studyguide.pk www.studyguide.
Calculate, for the time www.studyguide.pk that the ball is in contact with the plate, www.studyguide. www.studyguide.pk (i) the average force, in addition to the weight of the ball, that the plate exerts on the ball, www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. magnitude of force = .................................... N www.studyguide.pk www.studyguide.pk www.studyguide. direction of force = ........................................
[4]
www.studyguide.pk www.studyguide.pk www.studyguide.
(ii) the loss in kinetic energy of the ball. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. loss = ....................................... J [2] www.studyguide.pk www.studyguide.pkthe bounce.
(c) State and explain whether linear momentum is conserved during www.studyguide.
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www.studyguide.pk www.studyguide.pk www.studyguide.
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www.studyguide.pk www.studyguide.pk www.studyguide.
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.................................................................................................................................... [3] www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.
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www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk cliff and throws a ball vertically upwards withwww.studyguide. www.studyguide.pk a speed of 12 m s ,
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A girl stands at the top of a as illustrated in Fig. 3.1. www.studyguide.pk www.studyguide.pk www.studyguide. path of www.studyguide.pk www.studyguide.pk www.studyguide. ball www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. h www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.
Fig. 3.1 www.studyguide.pk www.studyguide.pk www.studyguide.
At the time that the girl throws the ball, her hand is a height h above the horizontal ground at the base of the cliff.
The variation with time t of www.studyguide.pk www.studyguide.pk the speed v of the ball is shown in Fig. 3.2. www.studyguide.
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www.studyguide.pk www.studyguide.pk www.studyguide. v/ms www.studyguide.pk www.studyguide.pk www.studyguide.
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t/s www.studyguide.pk www.studyguide.pk www.studyguide.
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Fig. 3.2 www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.
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www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.
Speeds in the upward direction are shown as being positive. Speeds in the downward direction are negative. www.studyguide.pk www.studyguide.pk www.studyguide.
(a) State the feature of Fig. 3.2 that shows that the acceleration is constant. www.studyguide.pk www.studyguide.pk www.studyguide.
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(b) Use Fig. 3.2 to determine the time at which the ball www.studyguide.pk www.studyguide.pk www.studyguide.
(i) reaches maximum height, www.studyguide.pk www.studyguide.pk www.studyguide. time = ………………………………. s www.studyguide.pk the base of the cliff. www.studyguide.pk www.studyguide.
(ii) hits the ground at time = ………………………………. s www.studyguide.pk www.studyguide.pk www.studyguide.
[2]
www.studyguide.pk www.studyguide.pk www.studyguide.
(c) Determine the maximum height above the base of the cliff to which the ball rises. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. height = …………………………… m [3] www.studyguide.pk www.studyguide.pk www.studyguide.
(d) The ball has mass 250 g. Calculate the magnitude of the change in momentum of the ball between the time www.studyguide.pk www.studyguide.pkthat it leaves the girl’s hand to time t = 4.0 s. www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. change = …………………………… N s [3] www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.
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www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.
(e) (i) State the principle of conservation of momentum.
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www.studyguide.pk www.studyguide.pk www.studyguide.
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www.studyguide.pk www.studyguide.pk www.studyguide.
............................................................................................................................. [2] www.studyguide.pk www.studyguide.pk www.studyguide.
(ii) Comment on your answer to (d) by reference to this principle. www.studyguide.pk www.studyguide.pk www.studyguide.
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www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.
8
A bullet of mass 2.0 g is fired horizontally into a block of wood of mass 600 g. The block is suspended from strings so that it is free to move in a vertical plane.
The
The bullet buries itself in www.studyguide.pk www.studyguide. www.studyguide.pktheinblock.3.1. block and bullet rise together through a vertical distance of 8.6 cm, as shown Fig. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. wood block www.studyguide.pk www.studyguide.pk www.studyguide. bullet www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.
8.6 cm www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.
Fig. 3.1
(a) (i) Calculate the change in gravitational potential energy of the www.studyguide.pk www.studyguide.pkblock and bullet. www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. change = ............................................. J [2]
(ii) Show that the initial www.studyguide.pk m sspeed of the block and the bullet, after they began to move off www.studyguide.pk www.studyguide. together, was 1.3
.
www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.
[1]
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www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.
(b) Using the information in (a)(ii) and the principle of conservation of momentum, determine the speed of the bullet before the impact with the block. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. speed = ....................................... m s [2] www.studyguide.pk www.studyguide.pk www.studyguide.
(c) (i) Calculate the kinetic energy of the bullet just before impact. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. kinetic energy = .............................................. J [2] www.studyguide.pk www.studyguide.pk www.studyguide.
(ii) State and explain from your answers www.studyguide.pk what can be deducedand the block. to (c)(i) and (a)(i) about www.studyguide.pk www.studyguide. the type of collision between the bullet
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www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pkheld on a horizontal surface by means of two springs, as shown in
9
A trolley of mass 930 g is www.studyguide.pk www.studyguide.
Fig. 4.1. www.studyguide.pk www.studyguide.pk www.studyguide. trolley spring www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.
Fig. 4.1 www.studyguide.pk www.studyguide.pk www.studyguide.
The variation with time t of the speed v of the trolley for the first 0.60 s of its motion is shown in Fig. 4.2. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.
8.0
www.studyguide.pk www.studyguide.pk www.studyguide. v / cm s www.studyguide.pk www.studyguide.pk www.studyguide.
6.0
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4.0
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2.0
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0
0.2
0.3
0.4
0.5
0.6
0
0.1 t/s www.studyguide.pk www.studyguide.pk www.studyguide.
Fig. 4.2 www.studyguide.pk www.studyguide.pk www.studyguide.
(a) Use Fig. 4.2 to determine
(i) the initial acceleration of the trolley, www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. acceleration = ………………………. m s [2] www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.
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www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.
(ii) the distance moved during the first 0.60 s of its motion. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. distance = ………….………………… m [3] www.studyguide.pk www.studyguide.pk www.studyguide.
(b) (i) Use your answer to (a)(i) to determine the resultant force acting on the trolley at time t = 0. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. force = …………………………….. N [2]
(ii) Describe qualitatively the variation with time of the resultant force acting on the www.studyguide.pk www.studyguide.pk www.studyguide. trolley during the first 0.60 s of its motion. www.studyguide.pk www.studyguide.pk www.studyguide.
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www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk work.
10
(a) Explain the concept of www.studyguide.pk www.studyguide.
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..................................................................................................................................... [2] www.studyguide.pk www.studyguide.pkvariation of the kinetic www.studyguide. (b) A table tennis ball falls vertically through air. Fig. 8.1 shows the energy E of the ball with distance h fallen. The ball reaches the ground after falling www.studyguide.pk. www.studyguide.pk www.studyguide. through a distance h energy www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.
E
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0
h
0
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Fig. 8.1 www.studyguide.pk www.studyguide.pk www.studyguide.
(i) Describe the motion of the ball. www.studyguide.pk www.studyguide.pk www.studyguide.
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(ii) On Fig. 8.1, draw a www.studyguide.pkball.line hto=show the variation with his of the gravitational potential
[3]
At h , the potential energy zero. energy E of the www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.
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K

0

K

P

0

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www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk by the internal energy of a substance. www.studyguide.
11
(a) Explain what is meant www.studyguide.pk
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(b) State and explain, in increases, decreases or does not change. www.studyguide.pk www.studyguide.pk www.studyguide.
(i) a lump of iron as it is cooled www.studyguide.pk www.studyguide.pk www.studyguide.
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.............................................................................................................................. [3] www.studyguide.pkevaporates at constant temperature www.studyguide.pk www.studyguide.
(ii) some water as it www.studyguide.pk www.studyguide.pk www.studyguide.
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www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pkby www.studyguide.pk www.studyguide.
12
(a) Define what is meant
(i) work done, www.studyguide.pk www.studyguide.pk www.studyguide.
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(ii) power.
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(b) A force F is acting on body that is moving with velocity v in the direction of the force. www.studyguide.pkawww.studyguide.pk www.studyguide.
Derive an expression www.studyguide.pkrelating the power P dissipated by the force towww.studyguide. www.studyguide.pk F and v. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.
[2]
(c) A car of mass 1900 kg www.studyguide.pk in 8.1 s. www.studyguide.pk accelerates from rest to a speed of 27 m s www.studyguide.
(i) Calculate the average rate at which kinetic energy is supplied to the car during the www.studyguide.pk www.studyguide.pk www.studyguide. acceleration. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. rate = ………………………. W [2] www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.
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www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pkprovides power at a constant rate. Suggest and explain why the www.studyguide.pk www.studyguide.
(ii) The car engine acceleration of the car is not constant. www.studyguide.pk www.studyguide.pk www.studyguide.
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www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pkspeed of a trolley as it rolls down a slope, as illustrated in Fig. 2.1.
13 A student investigates the www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. speed sensor www.studyguide.pk www.studyguide.pk www.studyguide. trolley www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.
Fig. 2.1 www.studyguide.pk www.studyguide.pk www.studyguide.
The speed v of the trolley measured using a speed sensor for different values of the time t www.studyguide.pkiswww.studyguide.pk www.studyguide. that the trolley has moved from rest down the slope.
Fig. 2.2 shows the variation with t of v. www.studyguide.pk www.studyguide.pk www.studyguide.
2.0
www.studyguide.pk www.studyguide.pk www.studyguide. v/ms www.studyguide.pk www.studyguide.pk www.studyguide.
1.5
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1.0
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0.5
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0
www.studyguide.pk www.studyguide.pk 1.0 www.studyguide. 0.4
0.6
0.8
0
0.2
1.2
t/s www.studyguide.pk www.studyguide.pk www.studyguide.
Fig. 2.2 www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.
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www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.
(a) Use Fig. 2.2 to determine the acceleration of the trolley at the point on the graph where t = 0.80 s. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. acceleration = ………………………… m s [4] acceleration is increasing
(b) (i) State whether the www.studyguide.pk www.studyguide. www.studyguide.pk your answer by reference toor decreasing for values of t greater than 0.6 s. Justify
Fig. 2.2. www.studyguide.pk www.studyguide.pk www.studyguide.
...................................................................................................................................
................................................................................................................................... www.studyguide.pk www.studyguide.pk www.studyguide.
.............................................................................................................................. [2] www.studyguide.pk www.studyguide.pk www.studyguide.
(ii) Suggest an explanation for this change in acceleration. www.studyguide.pk www.studyguide.pk www.studyguide.
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.............................................................................................................................. [1] www.studyguide.pk www.studyguide.pk www.studyguide.
(c) Name the feature of Fig. 2.2 that indicates the presence of www.studyguide.pk www.studyguide.pk www.studyguide.
(i) random error, www.studyguide.pk www.studyguide.pk www.studyguide.
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www.studyguide.pk www.studyguide.pk www.studyguide.
.............................................................................................................................. [1]
(ii) systematic error. www.studyguide.pk www.studyguide.pk www.studyguide.
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.............................................................................................................................. [1] www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.
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www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pkg www.studyguide.pk cliff with a speed of
14
(a) A stone of mass 56 is thrown horizontally from the top of a www.studyguide.
18 m s , as illustrated in Fig. 4.1. www.studyguide.pk www.studyguide.pk www.studyguide.
18 m s www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.
16 m www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. sea level www.studyguide.pk www.studyguide.pk www.studyguide.
Fig. 4.1 www.studyguide.pk www.studyguide.pkAir resistance may be www.studyguide. The initial height of the stone above the level of the sea is 16 m. neglected. www.studyguide.pk www.studyguide.pk www.studyguide.
(i) Calculate the change in gravitational potential energy of the stone as a result of falling through 16 www.studyguide.pk m. www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. change = ............................................... J [2]
(ii) Calculate the total kinetic energy of the stone as it reaches the sea. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. kinetic energy = .............................................. J [3] www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.
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www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pkas it hits the water is
(b) Use your answer in (a)(ii) to show that the speed of the stone www.studyguide. approximately 25 m s . www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.
[1]
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(c) State the horizontal velocity of the stone as it hits the water. www.studyguide.pk www.studyguide.pk www.studyguide. horizontal velocity = .........................................m s [1] www.studyguide.pk www.studyguide.pkthe horizontal velocity www.studyguide. (d) (i) On the grid of Fig. 4.2, draw a vector diagram to represent and the resultant velocity of the stone as it hits the water.
[1]
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Fig. 4.2 www.studyguide.pkdiagram to determine the angle with the horizontal at which the www.studyguide.pk www.studyguide.
(ii) Use your vector stone hits the water. www.studyguide.pk www.studyguide.pk www.studyguide. angle = .............................................. ° [2] www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.
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www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pkatwww.studyguide.pk0,www.studyguide. 15 A girl G is riding a bicycle a constant velocity of 3.5 m s . At time t = she passes a boy B sitting on a bicycle that is stationary, as illustrated in Fig. 2.1. www.studyguide.pk www.studyguide.pk www.studyguide.
B
www.studyguide.pk www.studyguide.pk www.studyguide.
3.5 m s
G
www.studyguide.pk www.studyguide.pk www.studyguide. t=0 www.studyguide.pk www.studyguide.pk www.studyguide.
Fig. 2.1 www.studyguide.pk www.studyguide.pk www.studyguide.
At time t = 0, the boy sets off to catch up with the girl. He accelerates uniformly from time t = 0 until he reaches a speed of 5.6 m s in a time of 5.0 s. He then continues at a constant speed of 5.6 m s . At time t = T, the boy catches up with the girl. www.studyguide.pk www.studyguide.pk www.studyguide.
T is measured in seconds. www.studyguide.pk www.studyguide.pk catches up with her.
(a) State, in terms of T, the distance moved by the girl before the boy www.studyguide. distance = ............................. m [1] www.studyguide.pk www.studyguide.pk www.studyguide.
(b) For the boy, determine www.studyguide.pk www.studyguide.pk www.studyguide.
(i) the distance moved during his acceleration, www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. distance = ............................. m [2] www.studyguide.pk www.studyguide.pk www.studyguide.
(ii) the distance moved during the time that he is moving at constant speed.
Give your answer www.studyguide.pk in terms of T. www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. distance = ................................. m [1] www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.
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www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk(a) and (b) to determine the time T taken forwww.studyguide.
(c) Use your answers in www.studyguide.pk the boy to catch up with the girl. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.
T = .......................................... s [2]
(d) The boy and the bicycle have a combined mass of 67 kg. www.studyguide.pk www.studyguide.pk www.studyguide.
(i) Calculate the force required to cause the acceleration of the boy. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. force = .......................................... N [3]
(ii) At a speed of 4.5 m s , the total resistive force acting on the boy and bicycle is www.studyguide.pk www.studyguide.pk www.studyguide.
23 N.
Determine the output power of the boy’s legs at this speed. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. power = ......................................... W [2] www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.
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www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pkenergy. 16
(a) (i) Define potential www.studyguide.pk www.studyguide.
..................................................................................................................................
www.studyguide.pk www.studyguide.pk www.studyguide.
............................................................................................................................. [1] www.studyguide.pk www.studyguide.pk www.studyguide.
(ii) Distinguish between gravitational potential energy and elastic potential energy. www.studyguide.pk www.studyguide.pk www.studyguide. gravitational potential energy ................................................................................... www.studyguide.pk www.studyguide.pk www.studyguide.
..................................................................................................................................
elastic potential energy ............................................................................................ www.studyguide.pk www.studyguide.pk www.studyguide.
............................................................................................................................. [2] www.studyguide.pk www.studyguide.pk www.studyguide.
(b) A small sphere of mass 51 g is suspended by a light inextensible string from a fixed point P. www.studyguide.pk www.studyguide.pk www.studyguide.
The centre of the sphere is 61 cm vertically below point P, as shown in Fig. 3.1. www.studyguide.pk www.studyguide.pk www.studyguide.
P
www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.
18°
61 cm sphere, www.studyguide.pk www.studyguide.pk www.studyguide. mass 51g www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.
Fig. 3.1
The sphere is moved to keeping www.studyguide.pkthe one side,Calculate the string taut, so that the string makes www.studyguide.pk www.studyguide. an angle of 18° with vertical. www.studyguide.pk www.studyguide.pk www.studyguide.
(i) the gain in gravitational potential energy of the sphere, www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. gain = ……………………….. J [2] www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.
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www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.
(ii) the moment of the weight of the sphere about point P. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. moment = .................................... N m [2] www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.
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www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pkcontents have a total mass of 42 kg. The trolley is being pushed www.studyguide.pk www.studyguide.
17 A shopping trolley and its along a horizontal surface at a speed of 1.2 m s . When the trolley is released, it travels a www.studyguide.pk www.studyguide.pk www.studyguide. distance of 1.9 m before coming to rest.
(a) Assuming that the total force opposing the motion of the trolley is www.studyguide.pk www.studyguide.pkconstant, www.studyguide. (i) calculate the deceleration of the trolley, www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. deceleration = ........................................... m s [2] www.studyguide.pk www.studyguide.pk16 N.
(ii) show that the total force opposing the motion of the trolley is www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.
[1]
www.studyguide.pk www.studyguide.pk www.studyguide.
(b) Using the answer in (a)(ii), calculate the power required to overcome the total force www.studyguide.pkof www.studyguide.pk www.studyguide. opposing the motion the trolley at a speed of 1.2 m s . www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. power = ........................................... W [2] www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.
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www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.
(c) The trolley now moves down a straight slope that is inclined at an angle of 2.8° to the horizontal, as shown in Fig. 3.1. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.
2.8°
www.studyguide.pk www.studyguide.pk www.studyguide.
Fig. 3.1 www.studyguide.pk www.studyguide.pk www.studyguide.
The constant force that opposes the motion of the trolley is 16 N. www.studyguide.pk www.studyguide.pk www.studyguide.
Calculate, for the trolley moving down the slope,
(i) the component down the slope of the trolley’s weight, www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. component of weight = ........................................... N [2] www.studyguide.pk www.studyguide.pk www.studyguide.
(ii) the time for the trolley to travel from rest a distance of 3.5 m along the length of the slope. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. time = ............................................ s [4] www.studyguide.pk www.studyguide.pkslope is not made any www.studyguide. (d) Use your answer to (c)(ii) to explain why, for safety reasons, the steeper. www.studyguide.pk www.studyguide.pk www.studyguide.
..........................................................................................................................................
www.studyguide.pk www.studyguide.pk www.studyguide.
...................................................................................................................................... [1] www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.
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www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk straight road at speed v. A hazard suddenlywww.studyguide. www.studyguide.pk appears in front of
18 A car is travelling along a the car. In the time interval between the hazard appearing and the brakes on the car coming into operation, the car moves forward a distance of 29.3 m. With the brakes applied, the front www.studyguide.pk www.studyguide.pk www.studyguide. wheels of the car leave skid marks on the road that are 12.8 m long, as illustrated in Fig. 2.1. www.studyguide.pk www.studyguide.pk www.studyguide. position of car skid mark when hazard appears www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.
29.3 m
12.8 m www.studyguide.pk www.studyguide.pk www.studyguide.
Fig. 2.1
It is estimated that, during the skid, the www.studyguide.pk of free fall. magnitude of the decelerationwww.studyguide. www.studyguide.pk of the car is 0.85 g, where g is the acceleration www.studyguide.pk www.studyguide.pk www.studyguide.
(a) Determine
(i) the speed v of the car before the brakes are applied, www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. v = …………………… m s [2] www.studyguide.pk www.studyguide.pk www.studyguide.
(ii) the time interval between the hazard appearing and the brakes being applied. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. time = ……………..…………. s [2] www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.
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www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pkonwww.studyguide.pk www.studyguide.
(b) The legal speed limit the road is 60 km per hour.
Use both of your answers in (a) to comment on the standard of the driving of the car. www.studyguide.pk www.studyguide.pk www.studyguide.
..........................................................................................................................................
www.studyguide.pk www.studyguide.pk www.studyguide.
..........................................................................................................................................
.......................................................................................................................................... www.studyguide.pk www.studyguide.pk www.studyguide.
..................................................................................................................................... [3] www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide. www.studyguide.pk www.studyguide.pk www.studyguide.
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