Energy and angular motion problem

[bdh2991]

Homework Statement

In the figure below, the hanging object has a mass of m1 = 0.355 kg; the sliding block has a mass of m2 = 0.840 kg; and the pulley is a hollow cylinder with a mass of M = 0.350 kg, an inner radius of R1 = 0.020 0 m, and an outer radius of R2 = 0.030 0 m. Assume the mass of the spokes is negligible. The coefficient of kinetic friction between the block and the horizontal surface is μk = 0.250. The pulley turns without friction on its axle. The light cord does not stretch and does not slip on the pulley. The block has a velocity of vi = 0.820 m/s toward the pulley when it passes a reference point on the table.

(a) Use energy methods to predict its speed after it has moved to a second point, 0.700 m away.

(b) Find the angular speed of the pulley at the same moment.

Homework Equations

KE = 1/2 mv^2 or 1/2 I ω^2

The Attempt at a Solution

For the first part i tried setting the kinetic energy of the block equal minus the energy lost to friction equal to the sum of the second masses kinetic energy added to the wheel's kinetic energy...i have way too many unknowns though an I'm not really sure what other equations to use...

 

[aralbrec]

If the block is moving at 0.820 m/s how fast is the pulley rotating? How fast is the vertically falling block moving?

Some time later you don't know how fast the block is moving, but you do know from the above that there is a relationship. Will that eliminate your unknowns?

 

[bdh2991]

If the block is moving at 0.820 m/s how fast is the pulley rotating? How fast is the vertically falling block moving?

Some time later you don't know how fast the block is moving, but you do know from the above that there is a relationship. Will that eliminate your unknowns?

the block vertically would be falling at the same rate that the block on the table is moving...correct?