Q. 71

Expert-verifiedFound in: Page 334

Book edition
4th

Author(s)
Randall D. Knight

Pages
1240 pages

ISBN
9780133942651

A cylinder of radius R, length L, and mass M is released from rest on a slope inclined at angle θ. It is oriented to roll straight down the slope. If the slope were frictionless, the cylinder would slide down the slope without rotating. What minimum coefficient of static

friction is needed for the cylinder to roll down without slipping?

Coefficient of friction is

A cylinder of radius= R,

length = L, and

mass = M is released from rest on a slope

angle of inclination= θ

Lets first draw the free body diagram as below

Equate horizontal and vertical force

As net force in perpendicular direction is zero so

N = mg cosθ ............................(1)

and

mg sinθ - f_{s} = ma ........................(2)

Where f_{s }is frictional force

Find the torque acting on cylinder.

As mass passes through axis of center so only frictional force will cause the torque

Torque is also expressed as

Substitute

Upon simplification

Now substitute the value of f_{s} in equation (1)

We know frictional force is

So

Substitute the value from equation(1) and (3)

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