What Mass Of Collision Took Place In Between The Block And The Stone?

Name:
Q1- (30 points)

During a physics lab, the student ask to add water to a bucket connect by a negligible mass rope to an 80.0 kg car which is positioned on a track which is inclined 15.00above the horizontal. The idea is illustrated in figure. Consider we are using a frictionless pulley. If the coefficient, between the car and the track is 0.200:
150
150

a- Draw the free body diagram and write the Newton’s second law equation for each body, car and bucket. (5 points) b- What mass of water would be needed to start the car moving up? (10 points) c- With friction present, suppose water is added until the car is just about move (calculated in part b). Now an additional 4.00 kg of water is added to the bucket with
the wheels of the car locked. When the wheels are unlocked, how long will it take the car to move 34.0 m up the track? (10 points) d- Explain with a specific example the first Newton’s laws and define what an inertial frame of reference is. (5points)

Extra Credit: e- What is the weight of a 50 kg mass object measure in an elevator traveling upward at constant acceleration of 5.0 m/s2? How much the weight changes if it is measured in the same elevator moving with the same acceleration but downward? (3 points)

Q2- (30 points) A 15.0 kg block is attached to a very light horizontal spring of force constant 500.0 N/m and is resting on a frictionless horizontal table. (See the figure). Suddenly it is struck by a 3.00 kg stone traveling horizontally at 8.00 m/s to the right, whereupon the stone rebounds at 2.00 m/s horizontally to the left. a- Calculate the speed of the block just after the collision with the stone.
(7 points) b- What kind of collision took place in between the block and the stone? Explain. (7 points) c- Find the maximum distance that the block will compress the spring after the collision. (7 points) d- Calculate the impulse of the block from the moment just after the collision to the moment when it the maximum compression of the spring occurs.(6 points) e- Identify and classify all forces acting on the block the moment when it the maximum compression of the spring occurs. Explain. (3 points) Extra Credit: f- A net force of 6 N acts on an object initially at rest for 0.25s and gives a final speed of 5 m/s. How could a net force of 2 N produce the same final speed?. Explain. (3 points)

Q3- (30 points)

A uniform 5.0 kg marble ball rolls without slipping down the path from point A to point B show in the figure, starting from rest. The marble balls travel a horizontal distance of 5.0 m after it left the path (from A to B), and before it hit the floor (following a projectile like motion).
4.0 m
4.0 m h = ? h = ?

h = 5.0 m
A
B

h = 5.0 m
A
B

a- Calculate the velocity, of the marble ball just at the moment of leave the path (A to B). (8 points) b- Calculate the height, (h) from where the marble start rolling dawn. (8 points) c- Calculate the mechanical energy of the ball at the end of the path (at point B). (5 points) d- Calculate the total work done from the starting position to the end of the path (from A to B). (5 points) e- Explain the concept of torque and the meaning of the moment of inertia.(4 points)

Extra Credit: f- For a primitive yo-yo, with a massless string around a solid cylinder with mass 200 g and radius 3.50 cm.
Find the downward acceleration of the cylinder and the tension in the string. (3 points)

Q4- (30 points)

A 5.0 kg and 2.0 m beam is hinged to a wall and supported by a thin cable attached to a building. The beam is supported at an angle of 400 as showed in the figure and used to support a 10 kg sign.

400 400

a- Draw the free body, diagram showing all forces. (5 points) b- Write the equilibrium, conditions applied to this situation (include each equation and the respectively lever arm for each force). (5 points) c- Calculate the tension in the cable. (7 points) d- Calculate the magnitude, of the compressive force exerted by the beam on the wall. (7 points)

Extra Credit:

e- If you exert a horizontal force of 0.20 N on the top surface (parallel to the surface) of a cube of Jell-O 6 cm, and observe a sideways displacement of 5 mm. What is the shear modulus of the Jell-O? (3 points)

Q6- (30 Points)

One mole of a monatomic ideal gas at p1, and V1is heated and expands at constant pressure to a volume 4V1. It is then cooled at constant volume until the pressure has dropped to half of initial pressure (0.5
p1).

a- Draw the pV- diagram and identify the thermodynamic processes involved. (5 Points) b- Calculate: (5 points)
- The total work done
- The change in internal energy
- The total heat c- Calculate the density, of three moles of this gas if, at a temperature of 300K, it exerts a pressure of 5 atm on the wall of a closed chamber. (Consider the molar mass of the gas equal to 5.0 g)(5 points) d- Calculate the heat, necessary to eliminated 150 g of water from a container which has 500 g of water. (5 points) e- State the first and second law of Thermodynamics. (5 points) f- A laboratory chamber contains about 150 moles of air. Find the change in the internal energy of the air when it is cooled from 25 oC to 68 oF at constant pressure. (Treat the air, as an ideal gas with γ=1.400).(5 points)

Extra Credit: g- Explain how you can determine the specific heat of a sample of unknown material using an example and including the respectively equation(s). (3 points)