Question

Two objects roll down a hill: a hoop and a solid cylinder. The hill has an elevation change of 1.4-m and each object has the same diameter (0.55-m) and mass. Calculate the velocity of each object at the bottom of the hill and rank them according to their speeds. [Hint: When an object is rolling, the angular speed and the velocity of the center of mass are related by ??cm = ??r, where ???? is the radius of the object.] cylinder = 4.3 ??/?? hoop = 3.7 ??/s NEED STEP BY STEP ANSWER pls.

Answer 1

When an object is rolling , the kinetic energy of object is sum of translationa and rotational kinetic energies.

Kinetic energy

For the hoop, moment of inertia about an axis passing through its center and perpendicular to its plane is

For solid cylinder , moment of inertia about an axis passing through its cylindrical axis is

------------------------

Initial energy of hoop at the top of the inclined plane is -------(1)

Kinetic energy of hoop at the bottom of the hill is

---------(2)

Conserving energy of the hoop at the top and bottom of hill,

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Initial energy of solid cylinder at the top of the inclined plane is -------(1)

Kinetic energy of solid cylinder at the bottom of the hill is

---------(2)

Conserving energy of the hoop at the top and bottom of hill,

So