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# A solid ball is released from rest and slides down a ISBN: 9780321675460 31

## Solution for problem 23E Chapter 10

University Physics | 13th Edition

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Problem 23E

A solid ball is released from rest and slides down a hill-side that slopes downward at 65.0o from the horizontal. (a) What minimum value must the coefficient of static friction between the hill and ball surfaces have for no slipping to occur? (b) Would the coefficient of friction calculated in part (a) be sufficient to prevent a hollow ball (such as a soccer ball) from slipping? Justify your answer. (c) In part (a), why did we use the coefficient of static friction and not the coefficient of kinetic friction?

Step-by-Step Solution:

Solution 23E Problem (a) Step 1: Consider the ball of radius R and mass M rolls down the hill. The angle between the slope and the horizontal = 65.0° To find the minimum value of the coefficient of static friction ( ) setween the hill and ball surfaces have for no slipping to occur. Consider the ball is a solid. Step 2: Many forces are acting on the ball as given in the diagram. Acceleration of the ball's center of mass is a and the magnitude of the friction force is f . The moment of CM inertia of the solid ball about its center of mass is I . CM Step 3: The equations of motion are F = Mg.sin + ( f ) = M.a ----(1) X CM Z =fR= ICM z-----(2) Where iszthe angular acceleration of the ball. g is acceleration due to gravity Friction forcef = Ns= Mgcos ----(3) Z = s R = I CM z----(4) Step 4: The ball rolls without slipping, therefore the acceleration of the ball's center of mass a CM = R -z---(5) Step 5: Solving (2) and (5) and eliminating z We get 2 a = fR ------(6) CM ICM Step 6: Solving (1) and (6) and eliminating...

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##### ISBN: 9780321675460

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