A solid homogeneous sphere of mass M = 3.90 kg is released from rest at the top

Question

A solid homogeneous sphere of mass M = 3.90 kg is released from rest at the top of an incline of height H=1.53 m and rolls without slipping to the bottom. The ramp is at an angle of ? = 26.5o to the horizontal.

1. Calculate the speed of the sphere's CM at the bottom of the incline.

2. Determine the rotational kinetic energy of the sphere at the bottom of the incline.

A solid homogeneous sphere of mass M = 3.90 kg is released from rest at the top of an incline of height H=1.53 m and rolls without slipping to the bottom. The ramp is at an angle of ? = 26.5o to the horizontal. 1. Calculate the speed of the sphere's CM at the bottom of the incline. 2. Determine the rotational kinetic energy of the sphere at the bottom of the incline.

Explanation / Answer

mgh =1/2mv^2 +1/2Iw^2 mgh =1/2 mv^2 +1/2 *2/5mr^2*(v/r)^2 2mgh =7/5 mv^2 hence v = 4.63 m/s rotational ke =1/2Iw^2 =1/2 *2/5mr^2*(v/r)^2 =1/5mv^2 =16.71 J

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