A light cable is wrapped around a solid cylinder with mass M = 1.50 kg and...
A light cable is wrapped around a solid cylinder with mass M = 1.50 kg and radius R = 0.20 m as shown in the figure below. The cylinder rotates with negligible friction about a stationary horizontal axis. The free end of the cable is tied to a block of mass m = 0.50 kg. The block, initially at rest, is released at a height h = 1.00 m above the floor. As the block falls, the cable unwinds without stretching or slipping, turning the cylinder. The mass of the cable as well as possible changes in the moment of inertia due to the unwinding can be ignored.
a) Write Newton's second law for the block.
b) Write Newton's second law for the rotational motion of the cylinder.
c) Using the equations from parts a and b, determine the acceleration of the block and the magnitude of the tension force.
d) Now, since you have determined the acceleration of the block and you know the initial speed and he initial height of the block above the floor, determine the speed of the block just as it hits the floor. Use a kinematics equation to solve this problem.
e) Determine the speed of the block just before it strikes the floor again using conservation of energy. Compare your result with the result you got in part d.
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