Avery light string is wound around a cylindrical spool of inertia m and radius r. the cylinder rotates on a frictionless horizontal axis with a moment of inertia 1mr2. attached to the end of the string is a block of inertia 2m, which pulls on the string and unwinds it from the cylinder, as the block falls.

(a) draw an extended free-body diagram for the cylinder, and a regular free-body diagram for the block.
(b) let m = 5kg, m = 2kg, and r = 6cm. what is the acceleration of the block as it falls?
(c) what is the tension on the string?
(d) after the block has dropped 30cm, starting from rest, what is the total kinetic energy of the system, and how is it distributed between the block and the cylinder?

While you are driving in the lane next to the curb on a multi-lane road the car on your left suddenly moves toward you lane. they are about toy crash into your front fender. you

Aspacecraft that renters the earth’s atmosphere drastically slows down. the amount of kinetic energy the spacecraft has as it reenters the earths atmosphere

Industrial processes often require the damping of vibrations. consider a workbench that uses four large ideal springs in place of traditional legs, with each spring supporting one corner of the workbench and exhibiting a force constant of 47500 n/m. this workbench is used when creating products that involve highly unstable chemicals. according to specifications, the acceleration of the manufacturing equipment must be held to less than 22.3 m/s2 for the manufacturing process to proceed safely. the amplitude of vibrations are expected to remain under 0.622 mm throughout. given that the workbench and maufacturing equipment combine to 6.05 kg, find the maximum acceleration expected of the equipment and workbench. (ignore the mass of the springs.)