# Physics: Problems and Solutions

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.

#### 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.