(a)
The change in momentum of the baseball during the process.
(a)
Answer to Problem 1SP
The change in momentum of the baseball during the process is
Explanation of Solution
Given info: The velocity of the ball before coming in contact with the bat is
Take initial direction of motion of the baseball to be positive.
Write the expression to find the initial momentum of the baseball.
Here,
Substitute
Write the expression to find the final momentum of the baseball.
Here,
Substitute
The negative sign is due to the fact that the final momentum is in negative direction.
Write the expression for change in momentum of the baseball.
Here,
Substitute
Conclusion:
Therefore, the change in momentum of the baseball during the process is
(b)
Whether the change in momentum is greater than the final momentum.
(b)
Answer to Problem 1SP
Yes, the change in momentum is greater than the final momentum.
Explanation of Solution
Linear momentum is the product of mass of an object and its velocity. It was called as the change in quantity of the motion. It is a vector and it has the same direction as that of velocity.
The change in momentum is found by taking the difference between the initial and the final values of momentum. If the change in momentum is greater than final momentum it must mean that the initial and final momentum have opposite directions.
The change in momentum is found to be
Conclusion:
Therefore, the change in momentum is greater than the final momentum.
(c)
The magnitude of impulse required to make the change in momentum.
(c)
Answer to Problem 1SP
The magnitude of impulse required to make the change in momentum is
Explanation of Solution
Given info: The change in momentum experienced by the baseball is
Write the expression for relation connecting the impulse and change in momentum of the baseball.
Substitute
Conclusion:
Therefore, the magnitude of impulse required to make the change in momentum is
(d)
The magnitude of average force that acts on the baseball to produce the impulse.
(d)
Answer to Problem 1SP
The magnitude of average force that acts on the baseball to produce the impulse is
Explanation of Solution
Write the expression for the impulse associated with the ball.
Here,
Rewrite the above equation for
Substitute
Conclusion:
Therefore, the magnitude of average force that acts on the baseball to produce the impulse is
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