Question
Select the correct answer.
Shelly rolls ball A in the positive x direction with a velocity of 7.5 meters/second. It hits stationary ball B and they undergo elastic collision. The two balls have different masses. Which of the following statements is true?
A.
the sum of their x–momentums must be equal to zero.
B.
the sum of their y–momentums must be equal to zero.
C.
the sum of their x–velocities must be equal to zero.
D.
the sum of their y–velocities must be equal to zero.
Shelly rolls ball A in the positive x direction with a velocity of 7.5 meters/second. It hits stationary ball B and they undergo elastic collision. The two balls have different masses. Which of the following statements is true?
A.
the sum of their x–momentums must be equal to zero.
B.
the sum of their y–momentums must be equal to zero.
C.
the sum of their x–velocities must be equal to zero.
D.
the sum of their y–velocities must be equal to zero.
Answers
Answered by
GPT-4o mini
In an elastic collision, the momentum is conserved in all directions. However, since the problem specifically mentions that ball A is rolled in the positive x direction and ball B is stationary, we need to consider the x-direction momentum.
Let's analyze the provided options:
A. The sum of their x–momentums must be equal to zero.
- This statement is false. The total x-momentum after the collision will equal the initial x-momentum, but it will not equal zero unless both objects are at rest after the collision.
B. The sum of their y–momentums must be equal to zero.
- This statement is incorrect as well. The y-momentum isn't directly involved in this scenario since both balls have no initial y-momentum, but momentum in the y-direction should still be conserved.
C. The sum of their x–velocities must be equal to zero.
- This statement is false. The sum of their x-velocities is not required to be zero. Instead, you will have an initial momentum from ball A, which will change after the collision.
D. The sum of their y–velocities must be equal to zero.
- This statement is also false given that there's no initial y-direction movement involved.
Since none of these statements directly reflect the conservation of momentum in this elastic collision scenario correctly, let's clarify:
In the context of elastic collisions, a more accurate statement would be that the total momentum in the x-direction before the collision must equal the total momentum in the x-direction after the collision, but none of the given options state this correctly.
Thus, the answer is that all of these statements are incorrect within the context of elastic collisions involving the balls as described.
Let's analyze the provided options:
A. The sum of their x–momentums must be equal to zero.
- This statement is false. The total x-momentum after the collision will equal the initial x-momentum, but it will not equal zero unless both objects are at rest after the collision.
B. The sum of their y–momentums must be equal to zero.
- This statement is incorrect as well. The y-momentum isn't directly involved in this scenario since both balls have no initial y-momentum, but momentum in the y-direction should still be conserved.
C. The sum of their x–velocities must be equal to zero.
- This statement is false. The sum of their x-velocities is not required to be zero. Instead, you will have an initial momentum from ball A, which will change after the collision.
D. The sum of their y–velocities must be equal to zero.
- This statement is also false given that there's no initial y-direction movement involved.
Since none of these statements directly reflect the conservation of momentum in this elastic collision scenario correctly, let's clarify:
In the context of elastic collisions, a more accurate statement would be that the total momentum in the x-direction before the collision must equal the total momentum in the x-direction after the collision, but none of the given options state this correctly.
Thus, the answer is that all of these statements are incorrect within the context of elastic collisions involving the balls as described.
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