A system of two paint buckets connected by a lightweight rope is released from rest with the 12.0-kg bucket 2.00 m above the floor. Use the principle of conservation of energy to find the speed with which this bucket strikes the floor. You can ignore friction and the mass of the pulley.

If R = 22.3 cm, M = 275 g, and m = 108 g in the figure, find the speed of the block after it has descended 12.9 cm starting from rest. Solve the problem using energy conservation principles.

In the figure here, a block of ice slides down a frictionless ramp at angle 0=56.0 ° while an ice worker pulls on the block (via a rope) with a force that has a magnitude of 58.0 N and is directed up the ramp. As the block slides down through distance d = 0.410 m along the ramp, its kinetic energy increases by 84.0 J. How much greater would its kinetic energy have been if the rope had not been attached to the block? F, Number i Unit

1. A 5.00-kg block is set into motion up an inclined plane with an initial speed of v; = 8.00 m/s. The block comes to rest after traveling 3.00 m along the plane, which is inclined at an angle of 30.0° to the horizontal. For this motion determine (a) the change in the block's kinetic energy, (b) the change in the potential energy of the block- Earth system, and (c) the friction force exerted on the block (assumed to be constant). (d) What is the coefficient of kinetic friction?