A bullet is fired into a block of wood sitting on a block of ice. The bullet has an initial velocity of 800 m/s and a mass of 0.007 kg. The wooden block has a mass of 1.3 kg and is initially at rest. The bullet remains embedded in the block of wood afterward.
- a. Assuming that momentum is conserved, find the velocity of the block of wood and bullet after the collision.
- b. What is the magnitude of the impulse that acts on the block of wood in this process?
- c. Does the change in momentum of the bullet equal that of the block of wood? Explain.
(a)
The velocity of the block of wood and bullet after collision.
Answer to Problem 2SP
The velocity of the block of wood and bullet after collision is
Explanation of Solution
Given info: The initial velocity of the bullet is
Write the expression for conservation of momentum.
Here,
Write the expression to find the initial momentum of the bullet.
Here,
Substitute
Write the expression to find the final momentum of the bullet and the wooden block.
Here,
Substitute
Write the expression for conservation of momentum.
Substitute
Conclusion:
Therefore, the velocity of the block of wood and bullet after collision is
(b)
The magnitude of the impulse that acts on the block of the wood.
Answer to Problem 2SP
The magnitude of the impulse that acts on the block of the wood is
Explanation of Solution
Write the expression for the final momentum of the wooden block.
Substitute
Write the expression for change in momentum of the wooden block.
Substitute
Write the expression of the impulse associated with the change in momentum.
Here,
Substitute
Conclusion:
Therefore, the magnitude of the impulse that acts on the block of the wood is
(c)
Whether the change in momentum of the bullet is equal to that of the block of the wood.
Answer to Problem 2SP
Yes, the magnitude of change in momentum of the bullet is equal to that of the block of the wood.
Explanation of Solution
Since the motion of the wooden block is due to the momentum imparted by the bullet, the magnitude of the change in momentum of the bullet is same as the change in momentum associated with the block of wood. The direction is opposite which facilitates the momentum conservation before and after the collision.
Conclusion:
Therefore, the magnitude of change in momentum of the bullet is equal to that of the block of the wood.
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Chapter 7 Solutions
Physics of Everyday Phenomena
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