A solid uniform cylinder of mass 3.25 kg, diameter 65.0 cm and length 12.4 cm, is connected to a block of mass 1.50 kg by a massless string passing over two frictionless pulleys, as shown below. The string is wrapped around the cylinder and doesn’t slip. The cylinder is free to rotate about an axis through its center perpendicular to its circular faces, and the system is released from rest. A. Draw free body diagrams for the cylinder and for the block. B. What is the acceleration of the block after it is released?
C. How far must the 1.50 kg block fall before it reaches a speed of 2.50 m/s?
D. How fast is the cylinder turning at this instant (i. e. at the instant the block is moving at 2.50 m/s)?
The rotational inertia of a solid cylinder of mass M and radius R rotating about its central axis is I = 2 1/2MR

The percent efficiency of a machine can never be 100% (or greater), because in the real world some energy is always converted into a. heat b. work c. input force d. output force

A23 kg log of wood begins from rest, 300 m up a sluice (a water track used to transport logs, think of it as an inclined plane with negligible friction) inclined at 20° to the horizontal. after it reaches the flat waterway at the bottom it collides elastically with a 100 kg block of wood initially at rest near the base of the incline. (a) how long does it take the 23 kg log to travel down the incline? (b) what is the speed of the 23 kg log at the bottom of the incline? (c) what are the velocities of both blocks of wood after the collision? (d) what is the total kinetic energy before the collision? (e) what is the kinetic energy of the 23 kg log after the collision? (f) what is the kinetic energy of the 100 kg block of wood after the collision? (g) what is the total kinetic energy after the collision? (h) compare the total initial and total final kinetic energies. is this consistent with what you would expect for elastic collisions? explain!

Aperson walks first at a constant speed of 4.89 m/s along a straight line from point a to point b and then back along the line from b to a at a constant speed of 2.95 m/s. what is the average speed over the entire trip?