A bowling ball rolls without slipping up a ramp that slopes upward at an angle β to the horizontal. treat the ball as a uniform, solid sphere, ignoring the finger holes.

a. What is the acceleration of the center of mass of the ball?
b. What minimum coefficient of static friction is needed to prevent slipping?

Question

09-12-2022
Physics

Answered

A bowling ball rolls without slipping up a ramp that slopes upward at an angle β to the horizontal. treat the ball as a uniform, solid sphere, ignoring the finger holes.

a. What is the acceleration of the center of mass of the ball?
b. What minimum coefficient of static friction is needed to prevent slipping?

Answer :

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abhinavjh321 abhinavjh321 · Answer 1 · 2022-12-17T23:31:33-05:00

The acceleration of the center of mass of the ball is a =g*sin(β)/1.4 and K=tanβ is the absolute minimum of the static friction coefficient.

A sort of opposition force known as frictional force attempts to counteract the motion of the body by acting on the surface of the body. Newton is its unit (N). It is described mathematically as the sum of the normal reaction and the coefficient of friction.

(a) A solid sphere rolling uphill has the equation of motion

M*g sinβ-(2/5)M*a = M*a, where an is the acceleration of the center of mass and mgcosβ = R.

We know that the static friction F=μR

By rearranging above formulas we get

2/5M*a + M*a = Mgsinβ

7/5a = gsinβ

Then a = gsinβ/1.4

(b) In the meantime, the normal force or maximum static friction force is equal to kmgcosβ, where k is the static friction's minimum coefficient. To prevent slippage, the frictional force must be less than the maximum static friction force.

Equating the two terms, we get: mgsinβ = kmgcosβ, k = (sinβ/cosβ) = tanβ.

As a result, k=tanβ is the lowest static friction coefficient.

To learn more about static friction click here https://brainly.com/question/13000653

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