Concept explainers
(a)
The distance moved by the ball
(a)
Answer to Problem 101P
Explanation of Solution
Given: Mass of the ball is
Radius of the ball is
The coefficient of kinetic friction between the ball and the floor is
At the instant the ball touches the floor it is moving horizontally with a speed
Formula used:
Velocity
Equation of kinematics
Where,
Calculation:
FIGURE:
In the figure
N is the normal reaction force which is acting in the upward direction through the point of contact.
Velocity
In this problem there arise a force of kinetic friction,
This acceleration is in the direction opposite to the direction of motion of the ball and hence equation
The horizontal force
Where,
Thus, the equation
Angular acceleration,
This angular acceleration sets the ball rotating with angular velocity
When the ball starts rolling, the velocity
is satisfied.
Substituting equation
Substituting for
Substituting the expression for
Substituting the value of
The distance moved by the ball
Using the equation
Substituting the expressions for
Conclusion:
The distance moved by the ball before it begin to roll without slipping is
Time taken by the ball to cover the distance
The final speed of the ball is
(b)
The ratio of the final kinetic energy to the initial kinetic energy of the ball.
(b)
Answer to Problem 101P
Explanation of Solution
Given: Mass of the ball is
Radius of the ball is
The coefficient of kinetic friction between the ball and the floor is
At the instant the ball touches the floor it is moving horizontally with a speed
Final velocity of the ball is
Formula used:
The final kinetic energy of the ball is given by,
Where,
Initial kinetic energy of the ball is given by,
Calculation:
Moment of inertia of the ball is given by,
For rotational motion of the ball the velocity,
Substituting for
But,
Therefore final kinetic energy of the ball is,
From equations
Conclusion:
The ratio of the final kinetic energy to the initial kinetic energy of the ball is
(c)
The values of
(c)
Answer to Problem 101P
Explanation of Solution
Given:
Formula used:
Calculation:
Substituting the numerical values in equation
Substituting the numerical values in equation
Substituting the numerical values in equation
Conclusion:
The values of
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Chapter 9 Solutions
Physics for Scientists and Engineers, Vol. 3
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