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Physics: Problems and Solutions

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1. In chronological order, what happens to the kinetic, potential, and total energy of the cart for one half cycle. The half cycle starts just after you have pushed the cart. The half cycle finishes just when the cart stops at the height of its motion. Remember, this is about the cart's mechanical energy.

A. Kinetic goes from zero to maximum (at the highest point of the incline.)
Potential goes from maximum to zero since the cart has stopped.
Total Energy rises as the cart gains altitude on the incline.
B. Kinetic goes from maximum to zero (at the highest point of the incline.)
Potential goes from zero to a maximum slightly less than Kinetic's maximum.
Total Energy stays the same, but decreases slightly due to friction.
C. Kinetic goes from zero to maximum (at the highest point of the incline.)
Potential goes from maximum to zero since the cart has stopped.
Total Energy stays "the same," but decreases slightly due to friction.
D. Kinetic stays constant because the cart is moving.
Potential starts out high because it has motion at the beginning and then goes to zero a the top since it stops.
Total Energy goes down because the cart is slowing down as it climbs the incline.
E. Kinetic goes from maximum to zero (at the highest point of the incline.)
Potential goes from zero to a maximum slightly less than Kinetic's maximum.
Total Energy rises as the cart gains altitude on the incline.

2. Which situation has the greatest magnitude of net force along incline? (By magnitude we mean |F|.)

A. the net force is always the same for an incline, f = mgcosθ
B. the net force is always the same for an incline, f = mgsinθ
C. when the cart is going downhill
D. when the cart is at rest
E. when the cart is going uphill

3. You have a level track. You push a cart with mass = 0.74[kg].
You measure the initial velocity to be 0.82[m s-1].
2 seconds later, you measure the velocity to be 0.615[m s-1].
What is the work (reported in mJ) that friction did on the cart?

4. You have a different system of unknown cart mass upon a level surface. The cart travels 165 [cm] in an unknown time period. The change in Kinetic Energy is -0.108845 [J]. What is the force of friction measured in Newtons?

5. What is the best way to determine levelness?

A. See if the Acceleration versus Time for both directions are both zero.
B. Plot Position versus Time and compare the linear fit from each direction of travel; slopes should be equal but opposite.
C. Plot Velocity versus Time for both directions; slopes should be equal.
D. Plot the Acceleration versus Time for one direction and acceleration should be zero.
E. See if slope of Velocity versus Time for both directions are equal but opposite.
F. Plot Position versus Time and compare the linear fit from each direction of travel; slopes should be equal.

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Solution Summary

This solution is comprised of detailed analysis of the given problems related to Mechanics and provides students with a clear perspective of the underlying concepts.

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Solving Physics Questions

1. Give an example of a situation in which there is a force and a non-zero displacement, but the force does no work. Explain why it does no work.
2. What is a conservative force?
3. (a) Calculate the work done on a 1500 kg elevator by its cable to lift it 40.0 m at constant speed, assuming friction averages 100 N. (b) What is the work done on the elevator by gravity in this process? (c) What is the total work done on the elevator?
4. A shopper pushes a grocery cart 20.0 m at constant speed on level ground, against a 35.0 N frictional force. He pushes in a direction 25.0 degrees below the horizontal. (A) What is the work done on the cart by friction? (B) What is the work done on the cart by gravity? (C) What is the work done on the cart by the shopper? (Remember the Work-Kinetic Energy Theorem.) (D) Find the force the shopper exerts, giving both the x- and y-components, and the magnitude of the force. (E) What is the total work done on the cart?
5. Compare the kinetic energy of a 20,000 kg truck moving at 110 km/h with that of an 80.0 kg astronaut in orbit moving at 27,500 km/h.
6. (a) Calculate the force needed to bring a 950 kg car to rest from a speed of 90.0 km/h in a distance of 120 m. Use the work-kinetic energy theorem (b) Suppose instead the car hits a concrete abutment at full speed and is brought to a stop in 2.00 m. Calculate the force exerted on the car and compare it with the force found in part (a).
7. Suppose a bicycle rolls down a hill, starting from rest. It drops an altitude of 4.0 m, ending up on level ground. The mass of the bicyclist plus bike is 70.0 kg. Assume that friction can be ignored. (A) Find the potential energy lost by the bicycle and rider. (B) Find the speed of the bicycle when it reaches level ground. (C) Repeat (B), assuming that this time the bicycle starts with an initial speed of 4.0 m/s. (D) Suppose frictional forces dissipate 400 J of energy while the bike rolls down the hill. Find the speed of the bicycle when it reaches level ground in this case. (Again, assume an initial speed of 4.0 m/s.)
8. A 60.0-kg skier with an initial speed of 12.0 m/s coasts up a 2.5-m-high hill as shown. (A) Find his final speed at the top, assuming no friction is involved. (Use energy methods, not the equations for constant acceleration.) (B) Now suppose the coefficient of friction between skier and snow is 0.08. Again find his speed at the top of the hill. (Don't worry about energy lost on the flat at either end --- just find the energy dissipated by friction on the 35-degree slope and use this in your calculations.)

9. A cart is rolling without friction on a platform, hooked to a hanging mass with a string which runs over a pulley, as shown in the diagram. The mass m_c of the cart is 0.35 kg, and the hanging mass is 0.050 kg. (A) How much work does the force of gravity do on the system when the hanging mass moves from a height of 0.80 m to a height of 0.30 m? (B) Assuming it starts from rest, find the speed of the cart after 0.50 m of travel. Use the information from part (A), and energy considerations. Do not use Newton's laws.

10. Suppose we have a spring whose force as a function of compression is shown in the graph. We place a ball of mass 0.600 kg on top of the spring and compress it by 0.25 m from its relaxed length. We then let the ball go. When the ball is released, its height above the floor is 0.10 m.

(A) Find the spring constant of the spring.
(B) Determine the potential energy of the spring when compressed.
(C) Find the highest point the ball reaches in its flight.
(D) Determine the velocity of the ball just as it leaves the spring: that is, just as the spring is fully relaxed.

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