I’m having trouble in my mechanical physics class with these problems about work-energy and friction.?

The setup is a block attached to a cart on a horizontal track with a pulley that has a hanging mass attached to it.?

I’m working on it right now but would really appreciate knowing if I’m properly setting up my equations and such.

Thank you.

? x=? y

Work against friction is:

? mc g ? y

P . E .=m H g ? y

1
K . E .= mH v 2
2

1.

For the system shown in the schematic, use the
Work/Energy Theorem to derive an expression for the
final velocity of the system assuming no frictional forces
are present.

? F=ma

mH g ? y=K . E .

W =? F ?dr

1
2 1
2
mH g ? y= mc v f ? mc v i
2
2

3. Use freebody analysis and the change in mechanical
energy of the system to derive an expression for the
coefficient of kinetic friction for the sliding block.

2. Now, use the Conservation of Energy argument to
derive an expression for the final velocity of the
system assuming friction is present.

Part 1:
1. From the data collected calculate the work done on the system .
2. Calculate the change in kinetic energy of the system.
Part 2:
1. For the run with the friction block on the cart, calculate ?K and ?U, the change in kinetic and potential energy
respectively. Is mechanical energy conserved?
2. Use the difference to determine the nominal frictional force acting on the system.
3. For the run with the block behind the cart calculate ?K and ?U, and determine the net frictional force acting on the
system. Then, determine the frictional force of the block itself.

4. Use freebody analysis to determine the coefficient of kinetic friction for this block. Compare with the accepted values.
Note: The accepted values for the coefficients of friction are: ? cork = 0.45, ?felt = 0.22 and ?plas = 0.16.