Some curious students hold a rolling race by rolling four items down a steep hil

Question

Some curious students hold a rolling race by rolling four items down a steep hill. The four items are a solid homogeneous sphere, a thin spherical shell, a solid homogeneous cylinder and a hoop with all its mass concentrated on the hoop's perimeter. All of the objects have the same mass and start from rest. Assume that the objects roll without slipping and that air resistance and rolling resistance are negligible. For each statement below, select True or False.

The hoop reaches the bottom of the hill before the homogeneous cylinder.

Upon reaching the bottom of the hill, the homogeneous sphere will have a larger rotational kinetic energy than any of the other objects will when they reach the bottom of the hill.

Explanation / Answer

Let h is the initial vertical height of startcing point.

then

final speeds,

v_solid sphere = sqrt(1.428*g*h)

v_holow sphere = sqrt(1.2*g*h)

v_cyllinder = sqrt(1.33*g*h)

v_hoop = sqrt(g*h)

1) B)flase

beacuse, clearly v_cyllinder > v_hoop

2) Flase

beacuse, it has larger linear kinetic energy.

so. it shoukd have lower rotational kinetic energy.

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.