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Chapter 6
Describe the “coin and feather” experiment and state what the observation shows. (5M)
Put a coin and a small paper disc in a glass tube (1M)
Use a vacuum pump to remove the air from the tube (1M)
Hold the tube vertically then invert it quickly. (1M)
The coin and the paper disc fall at the same rate (1M)
The experiment shows that objects with different masses fall at the same rate when there is no air resistance. (1M)

How can you find the height of a building if you are given a stopwatch and an iron ball? (3M)
First, release the ball from the top of the building (1M) and starts the stop watch at the same time to record the time required for the ball falling from the top of the building to the ground(1M).
The height of the building h is given by h=0.5gt^2 (1M)

Suggest four factors that would affect the deceleration of a car. (4M)
Braking force of the car (1M)
Number of passengers in the car/ mass of the car(1M)
Friction on the road (1M)
Gradient of the road (1M)

Chapter 7
Describe the procedures to prepare a friction-compensated runway. (5M)
Put an object onto a runway (1M)
Slowly increase the angle until the object slides down the runway. (1M)
Slightly decrease and adjust the angle until the object slides down with a constant velocity(1M) when a light push is given. (1M)
The motion of the object can be monitored by a ticker-tape timer or a motion sensor. (1M)

Describe briefly an experimental method to find the speed of the block at a certain small time interval.
The speed of the block can be measured by means of a ticker-tape timer. (1M)
Time interval can be found by the product of the number of dots chosen and the period of the vibrator.
Therefore, speed = length of the tape chosen Time interval for that length (1M)

You are provided with a runway and a data-logging system with a motion sensor. Describe how you should use the apparatus to conduct an experiment to demonstrate the relationship between the net force and the acceleration of a trolley. You may use additional apparatus if necessary (5M)
Adjust the runway for friction compensation (1M)
Pull a trolley down the runway using an elastic thread. Keep the extension of the elastic thread constant all the way. (1M)
Record the motion of the trolley with the data-logging system and find the acceleration of the trolley. (1M)
Repeat by pulling the trolley with 2, 3 and 4 identical elastic threads, side by side and extended by the same length as before. (1M)
From the experiment, it is found that the acceleration of the trolley is directly proportional to and in the same direction of the net force. (1M)

It is not preferable to carry an excessive amount of goods on the bicycle when he is riding in the street, why? (3M)
The larger the mass, the larger the inertia the bicycle has. (1M)
By newton’s second law of motion, the deceleration of the bicycle would become smaller when John applies the brake. (1M)
As a result, the stopping distance increases (1M)
So the chance of having an accident is larger.

In supermarkets, bottled drinks are usually stored in refrigerators with shelves inclined at an angle θ with the horizontal. Explain why there is such an arrangement. Also state the minimum angle required to achieve the purpose above. Given mass of a bottle ‘M’, friction between a 1-kg bottled drink and the inclined shelf is ‘f’. (3M)
If the bottled drinks are put on inclined shelves, they would slide down automatically when the first bottle is taken. It is more convenient for customers. (1M)
Mgsinθ > f (1M) θ> sin^-1 ( f/Mg) (1M)
Therefore, the least inclination angle is sin^-1 ( f/Mg).

In some parts of the world, it is common for people to shoot firearms straight up into the air during celebrations. Falling bullets pose a significant danger to bystanders. As a bullet falls, its velocity increases until it reaches a constant terminal velocity. Explain, in terms of forces acting on the bullet, why this happens. Also, assume the air resistance is bv , derive the terminal kinetic energy of the bullet. (5M)
As the bullet falls, its downward weight and the upward air resistance (or friction) are acting on it (1M)
Firstly the bullet accelerates.
The air resistance opposing the motion of the bullet increases with its velocity. (1M)
Finally, its weight is balanced by the air resistance at a certain velocity. (1M)
As the net force acting on the bullet is zero, the bullet will continue to fall at this constant velocity which is called terminal velocity. (mg = bv) (1M)
KE=0.5mv^2 = 0.5m^3 g^2 /b^2 (1M)

A basketball player jumps up such that his height reaches a height of 3m. Using Newton’s laws of motion, explain why the player can gain an initial speed to leave the ground vertically. (3M)
The player exerts a force onto the ground when he is about to jump. (1M)
This results an equal normal reaction force from the ground according to Newton’s 3rd law of motion. (1M)
As the normal reaction force is greater than the weight , the player will be forced to accelerate up according to Newton’s 2nd law of motion. (1M)

Chapter 8
What is the advantage of using the spanner扳手 to turn a screw螺絲?
(1) The effort(force) required can be reduced. ✓
(2) The efficiency can be increased. ✗
(3) The energy required can be reduced. ✗
For (2) and (3), they are wrong as moment is not related to energy. (Force is perpendicular to the displacement, the work done should be zero.)

Chapter 9
There are two methods of raising the block from the ground to a certain height. (2M)
Method 1 : Pulling the block up a inclined plane
Method 2 : Lifting the block vertically upwards.
Method 1 is better than method 2 in terms of forces as smaller force is needed to raise the block in method 1. (1M)
However, method 1 has a lower efficiency because some energy is lost in overcoming the friction between the block and the plane. (1M)

What are the functions of the counterweight in a lift system? (3M)
To reduce the power required to raise the car (1M)
To reduce the load acting on the motor (1M)
To improve the efficiency of the lift (As less energy is lost to overcome the friction between the cable line and the drum) (1M)

Verify the conservation of mechanical energy. Given a simple pendulum, a protractor, a light gate, a ruler. (7M)
Set up a simple pendulum, a protractor and a light gate. (1M)
Displace the bob and read the angle θ between the string and the vertical from the protractor. (1M)
Start data-logging and release the bob. (1M)
Record the time t taken for the bob to pass through the light gate. Measure the diameter of the bob(this is the distance travelled by the bob while passing the light gate, which is very small so the instantaneous speed of the bob in the lowest position calculated is relatively accurate), and hence estimate the speed v of the bob at the lowest position. (1M)
Use a ruler to measure the length l of the pendulum. Apply the conservation of mechanical energy and calculate the speed v of the bob at the lowest position. (1M)
V = {square root (2gh)} , where h = l(1-cosθ) (1M)
Conclusion, the two values of speed calculated is quite close so the law of conservation of energy is proved. (1M)
Precaution: the pendulum bob used should be heavy in a bid to minimize the effect of air resistance.

Chapter 10
What practical arrangement would you use in order to demonstrate inelastic and elastic collision respectively with two trolley? (2M)
For inelastic collision, a pin is fixed at the head of X and a cork is fixed at the tail of Y. (1M)
For elastic collision, one of the trolley has spring-loaded plunger installed. (1M)

Outline a method to measure an unknown mass(trolley B) in a place where there is no gravity. (5M)
Given: Trolley A with known mass , trolley B with unknown mass, a data logger system, a compressed and massless spring, a smooth horizontal surface.
Put 2 trolleys, namely trolley A and trolley B on a smooth horizontal surface. (1M)
Hold the two trolleys with a compressed, light spring( p.s. assume the spring is massless). (1M)
When the system is released from rest, the spring expands. (1M)
Record the motion of the 2 trolleys with a data-logging to find out their velocity. (1M)
By recording the velocity of the two trolleys, we can find the mass of trolley B by
(Mass of trolley A x velocity of trolley A) + (Mass of trolley B x velocity of trolley B) = 0 (1M)

State 3 designs on a vehicle which can reduce the degree of injury of the driver during impact. Explain briefly. (3M)
Seat belt is installed to prevent the driver impact to increase the duration of the impact so as to reduce the impact force. (1M)
Crumple zone of the car is collapsible during impact to increase the duration of the impact so as to reduce the impact force. (1M)
Airbag act as cushions to slow down the forward motions of the passengers due to inertia. This also helps to prevent the passengers from hitting the interior parts of cars. (p.s. For normal circumstance, the driver should sit at least 25cm from the steering wheel to give enough room for the airbag to inflate. (1M)
Explain how the crumple zone of a car can reduce the force of impact during collision. (4M)
In a collision, the crumple zone in the front section of the car collapses (1M)
As it is relatively deformable (1M)
As it collapses, the time of impact is lengthened. (1M)
And the force acting on the passenger is much reduced. (1M)

When a ball hit a wall, the wall doesn’t move, is momentum conserved in this case? (2M)
The momentum is still conserved. (1M) The wall doesn’t move simply because an external force acts on the plasticine by the ground(or the earth) during the collision. The wall just acquires a negligible speed after the collision. (1M)

A rocket is filled with water and compressed air. Explain why the rocket rises when the trigger is puller and name the law or principle involved. (3M)
When the trigger is pulled, the compressed air inside the rocket exerts a force on the water and forces the water out. (1M) By the principle of conservation of momentum (1M), the rocket acquires an upward momentum and rises. (1M)

A man falls vertically from the building of 15metres high. He is rescued by a cushion of thickness of 3.5m and being stopped 0.5m above the ground. If a thicker cushion is used, he is again stopped when he is 0.5m above the ground. Explain why a thicker cushion is better for rescuing the man? (3M)
As the potential energy loss is the same in both cases, (1M)
The distance travelled by the man in the thicker cushion is larger. (1M)
Therefore, the average resistive force by the cushion is smaller. (1M)

A block is situated in an inclined plane. If a gun shoots a bullet to the block and is embedded to the block, the block rises to a certain height. What would be the rise of the block if the bullet is shot with the same initial speed but rebound after hitting the block. (neglect air resistance.) (4M)
The maximum height of the block increases. (1M)
As the bullet rebounds, the change of momentum of the bullet increases. (1M)
According to the law of conservation of momentum, the gain of momentum of the block increases. (1M)
Therefore, the block rises to a higher level according to the law of conservation of energy. v = square root(2gh) (1M)

Chapter 12
Study the centripetal force using a conical pendulum. (6M)
Connect a rubber bung to a load by a string through a glass tube. Measure the masses m and M of the bung and the load respectively. (1M)
Stick a marker onto the string so that a length L of the string extends above the glass tube as shown. (1M)
Hold the tube vertically and whirl the bung around at a steady speed. Keep the marker just below the tube without touching it. (1M)
Ask your partner to time 50 revolutions of the bung and find its angular speed w. (1M)
Repeat the steps by choosing different lengths of L. (1M)
The centripetal force can be calculated as follows:
Tcosθ = mLw^2(cosθ) where θ is the angle between the string and the horizontal.
T = mLw^2 = Mg (1M)

A car performs circular motion in a circular bend. Explain why roads are not banked at a large angle in practice with a view to providing centripetal force for the car. (3M)
Although normal reaction can provide the car centripetal force to perform circular motion, it is dangerous for the driver. (1M) It is because if the inclination of the road is too steep(1M), there is a tendency for a car with low speed to turn inwards and it requires the driver to pay greater attention in manipulating the car at low speed. (1M) A donut-shaped space station is far from any planetary objects (i.e. assume this system is not affected by the attraction with other planetary objects). It is designed such that the astronauts live at the periphery 1.0km from the centre. Describe how an ‘artificial gravity’ of 10Nkg^-1 can be created at the periphery.(3M)
The space station should rotate about an axis through its centre and normal to the plane containing the station with a constant angular speed (1M) such that the centripetal acceleration at the periphery equals 10ms^-2. (1M) Equation : a=w^2 r (1M)
(note: GM/r^2 is wrong because an object only gives out gravitational field but cannot accelerate itself.

Are all people having the same linear speed, centripetal acceleration and angular speed on the earth no matter where they are? Assume that the earth is a perfect sphere. (6M)
All people on the earth are undergoing uniform circular motion. As the period of the earth’s rotation is 24 hours, all people should have the same angular speed given by w = 2π/T (2M)
However, the distances between different people and the rotational axis vary, depending on their location.
Therefore, their linear speed, which is given by v = rw should be different. (2M)
Also, their centripetal acceleration, which is given by a=rw^2 is also different. (2M)

Chapter 13
Explain briefly why the astronaut should lie down in a bed-shaped seat during launching. (2M)
As the supporting force is very large due to the huge acceleration required during launching(1M), the astronaut should lie down in a bed-shaped seat to reduce the pressure by increasing the contact area. ( F/A = P ) (1M)

A student explains that since the orbit is at a great distance from the earth, the acceleration due to gravity and the weight of the astronaut are both zero. Do you agree with the student? (3M)
No, at a point in an orbit of radius r,
Acceleration due to gravity = GME/r^2 ≠ 0 (1M)
Weight of the astronaut = GMEml/r^2 ≠ 0 (1M)
The astronaut is weightless because his weight (gravitational force) is completely used for centripetal acceleration, thus there is no supporting force. (1M)

In a space, two astronauts A and B approach each other in opposite directions, astronaut A carries with him a toolbox. Briefly describe what you would do in order to avoid collision. What is the minimum speed of the toolbox in this case. (3M)
Astronaut A can throw a toolbox to astronaut B. (1M)
In this case, some momentum of A is transferred to B by doing so. (1M)
Regarding the minimum speed of the toolbox, it can be achieved if and only if it is thrown at a speed so that eventually both Astronaut A and Astronaut B who has received the toolbox from Astronaut A move at the same velocity(same speed and in the same direction). OR( velocity of B > velocity of A) (1M)

Suggest two reasons why a Satellite A was not discovered from earth even though it is bigger than a Star B nearby which can be discovered from earth. (2M)
Satellite A is too close to Star B that it is lost in the glare of the reflected sunlight from the Star B. (1M)
Satellite A and Star B cannot be resolved(即無法分辨/解像resolution，) when observed from the earth.(1M)
What is the major assumption of the validity of the Kepler’s third law of planetary motion regarding a satellite orbiting around a planet?(2M)
Orbits of the satellites are circular. (1M)
Neglect the gravitational pull of nearby planets. (1M)