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The question reads:
17. For Experiment 2, how much the height of the block changes depends on:
I. the initial velocity of the bullet.
II. the mass of the block.
III. the length of the string.
A. I only
B. I and II only
C. II and III only
D. I, II, and III
Choice B is the best answer. The swinging of the block occurs after the collision, so we need to consider the block plus bullet after the collision. The block-bullet system has a maximum velocity right after the collision. If we apply conservation of energy to the swinging process, then we can relate the kinetic energy of the block-bullet system to gravitational potential energy using:
1/2 mv^2 = mgh therefore 1/2v^2 = gh
The mass cancels out of the equation, so the speed acquired as a result of the collision dictates the maximum height of the block-bullet system. This means that the speed of the bullet at impact affects the height to which the swings, so Statement I is valid. This eliminates choice C. However, the velocity after the collision depends on the mass of the block. By conservation of momentum, the initial momentum of the bullet is converted to the final momentum of the block and bullet:
mbullet*Vbullet= (mblock + mbullet)*Vbullet-block system
As the mass of the block increases, the velocity after the collision decreases. Hence, the mass of the block will affect the maximum height, so Statement II is valid. This eliminates choice A. The length of the string will impact the exact height of the block, but it does not impact the change in height, as that depends on energy, not position. Statement III is invalid, which eliminates choice D.
Using physical intuition to confirm our answer, we know that as the bullet goes faster, the block will inherit more speed and thus swing higher. We also know that it is easier to move lighter objects, so a lighter block can swing higher than a heavier block when pushed by the same force. The best answer is choice B.
Can someone please explain this to me? Why doesn't the length make a difference? At the end of the explanation they say you can get this question by physical intuition, but only discuss 2 of the 3 parameters and they don't describe using physical intuition with the length of the string/pendulum.
17. For Experiment 2, how much the height of the block changes depends on:
I. the initial velocity of the bullet.
II. the mass of the block.
III. the length of the string.
A. I only
B. I and II only
C. II and III only
D. I, II, and III
Choice B is the best answer. The swinging of the block occurs after the collision, so we need to consider the block plus bullet after the collision. The block-bullet system has a maximum velocity right after the collision. If we apply conservation of energy to the swinging process, then we can relate the kinetic energy of the block-bullet system to gravitational potential energy using:
1/2 mv^2 = mgh therefore 1/2v^2 = gh
The mass cancels out of the equation, so the speed acquired as a result of the collision dictates the maximum height of the block-bullet system. This means that the speed of the bullet at impact affects the height to which the swings, so Statement I is valid. This eliminates choice C. However, the velocity after the collision depends on the mass of the block. By conservation of momentum, the initial momentum of the bullet is converted to the final momentum of the block and bullet:
mbullet*Vbullet= (mblock + mbullet)*Vbullet-block system
As the mass of the block increases, the velocity after the collision decreases. Hence, the mass of the block will affect the maximum height, so Statement II is valid. This eliminates choice A. The length of the string will impact the exact height of the block, but it does not impact the change in height, as that depends on energy, not position. Statement III is invalid, which eliminates choice D.
Using physical intuition to confirm our answer, we know that as the bullet goes faster, the block will inherit more speed and thus swing higher. We also know that it is easier to move lighter objects, so a lighter block can swing higher than a heavier block when pushed by the same force. The best answer is choice B.
Can someone please explain this to me? Why doesn't the length make a difference? At the end of the explanation they say you can get this question by physical intuition, but only discuss 2 of the 3 parameters and they don't describe using physical intuition with the length of the string/pendulum.
