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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kumarprabhat kumarprabhat · Answer 1 · 2022-12-17T11:35:00-05:00

Friction is an opposition force acting on the surface of the body that tries to oppose the motion of the body. its unit is Newton (N) . The minimum coefficient of static friction is k= αtanβ.

It is a particular form of opposing force that is acting on the body's surface and seeks to stop the body from moving. its measure is in Newton (N). It is described mathematically as the result of the friction coefficient and normal reaction.

The equation becomes balanced once the specified force and acceleration have been resolved in each of the individual components.

X-directional components

On an incline, find the acceleration

Masina -F= ma

mgcosa =R

F=ur

Slippage must be prevented by a frictional force that is less than the maximum static friction force. We'll use constants like to represent the proportion between the opposite and adjacent sides of the ramp. At this point, ma equals the frictional force. Previously, a=gsin was found to exist. Equating both terms:

αmgsinβ = Kmgcosβ

K= α(sinβ/cosβ)

sinβ/cosβ= tanβ

k= αtanβ

Thus, the minimum coefficient of static friction is k= αtanβ.

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?

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