A solid ball of inertia m rolls without slipping down a ramp that makes an angle θ with the horizontal. a. What frictional force is exerted on the ball?
b. As a function of θ, what coefficient of friction is required to prevent slipping?

Question

09-12-2022
Physics

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A solid ball of inertia m rolls without slipping down a ramp that makes an angle θ with the horizontal. a. What frictional force is exerted on the ball?
b. As a function of θ, what coefficient of friction is required to prevent slipping?

Answer :

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kumarprabhat kumarprabhat · Answer 1 · 2022-12-17T11:24:45-05:00

A) f= 2/7mgsin∅ frictional force is exerted on the ball, B) u= 2/7gtan∅ coefficient of friction is required to prevent slipping. A solid ball of inertia m rolls without slipping down a ramp that makes an angle θ with the horizontal.

Part a)

Force equation is given as

mg sin∅-f= ma

now for torque equation of the ball

f R= 2/5 R²(a/R)

f=2/5 ma

now from above two equations

mg sin∅-2/5 ma=ma

mg sin∅+7/5 ma

a=5/7 g sin∅

so frictional force is given as

f=2/5 ma

f= 2/5m (5/7sin∅)

f=2/5 mg sin∅

Part b)

We also understand that when motion is moving normally, we have

Fn= mg cos∅

so we have

f=uFn

2/7 mg sin∅= u(mg cos∅)

now we have

u= 2/7 g tan∅

A solid ball of inertia m rolls without slipping down a ramp that makes an angle θ with the horizontal. a. What frictional force is exerted on the ball?b. As a function of θ, what coefficient of friction is required to prevent slipping?

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A solid ball of inertia m rolls without slipping down a ramp that makes an angle θ with the horizontal. a. What frictional force is exerted on the ball? b. As a function of θ, what coefficient of friction is required to prevent slipping?

Answer :

Other Questions

A solid ball of inertia m rolls without slipping down a ramp that makes an angle θ with the horizontal. a. What frictional force is exerted on the ball?
b. As a function of θ, what coefficient of friction is required to prevent slipping?