Concept explainers
A sphere of radius r and mass m has a linear velocity v0 directed to the left and no angular velocity as it is placed on a belt moving to the right with a constant velocity v1. If after first sliding on the belt the sphere is to have no linear velocity relative to the ground as it starts rolling on the belt without sliding, determine in terms of v1and the coefficient of kinetic friction
(a)
The value of
Answer to Problem 16.74P
Value of
Explanation of Solution
Given information:
Mass
Radius
Belt velocity
Ball velocity
Friction coefficient
Concept used:
Following formula is used-
1. Sum of horizontal forces,
2. Sum of moments about mass center,
Calculation:
Friction force:
Sum of horizontal forces;
Sum of moments about mass center:
Velocity equation,
Angular velocity equation,
Velocity of contact point,
Conclusion:
Thus we get,
Value of
(b)
The time at which sphere starts rolling.
Answer to Problem 16.74P
Value of time
Explanation of Solution
Given information:
Mass
Radius
Belt velocity
Ball velocity
Friction coefficient
Concept used:
Following formula is used-
1. Sum of horizontal forces,
2. Sum of moments about mass center,
Calculation:
Friction force:
Sum of horizontal forces:
Sum of moments about mass center:
Velocity equation:
Angular velocity equation:
Velocity of contact point:
Conclusion:
Thus we get,
Value of time
(c)
The distance moved by sphere relative of ground.
Answer to Problem 16.74P
Distance moved
Explanation of Solution
Given information:
Mass
Radius
Belt velocity
Ball velocity
Friction coefficient
Concept used:
Following formula is used-
1. Sum of horizontal forces,
2. Sum of moments about mass center,
Calculation:
Friction force,
Sum of horizontal forces,
Sum of moments about mass center,
Velocity equation,
Angular velocity equation,
Velocity of contact point,
Distance moved,
Conclusion:
Thus we get,
Distance moved
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Chapter 16 Solutions
Vector Mechanics For Engineers
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