The 9-ball travelling and strikes the 13-ball, which is of equal mass and at rest. If this is an elastic collision, which statement below is true? Marks 3+4 = 7
a) All of the 9-ball’s energy and momentum are transferred to the 13-ball.
b) All of the 9-ball’s energy and some of its momentum are transferred to the 13-ball.
c) Some of the 9-ball’s energy and all of its momentum are transferred to the 13-ball.
d) In this collision, momentum is not conserved.
e) In this collision energy, is not conserved.
Note: Select the best choice given above (a to e) according to your best of knowledge, and also write the reason of your selected choice as well.
The correct answer is option b) All of the 9-ball's energy and some of its momentum are transferred to the 13-ball.
The reason for this is that in an elastic collision, both momentum and kinetic energy are conserved. Since the 9-ball is traveling and strikes the 13-ball, it transfers some of its momentum to the 13-ball. However, not all of the momentum is transferred because part of the 9-ball's momentum is retained after the collision. The 9-ball also transfers some of its kinetic energy to the 13-ball, but not all of it, as some of the energy is also retained by the 9-ball. Therefore, option b) is the correct choice.
To determine the correct statement, we need to analyze what happens during an elastic collision.
In an elastic collision, both energy and momentum are conserved. This means that the total kinetic energy and the total momentum before the collision should be equal to the total kinetic energy and total momentum after the collision.
Let's now analyze the options:
a) All of the 9-ball’s energy and momentum are transferred to the 13-ball.
This statement is not true because in an elastic collision, both energy and momentum are conserved. All the energy and momentum of the 9-ball cannot be transferred to the 13-ball.
b) All of the 9-ball’s energy and some of its momentum are transferred to the 13-ball.
This statement is plausible because during an elastic collision, some of the energy and some of the momentum can be transferred from one ball to the other. Both energy and momentum are conserved.
c) Some of the 9-ball’s energy and all of its momentum are transferred to the 13-ball.
This statement is not true because, in an elastic collision, both energy and momentum are conserved. It is not possible for all of the momentum of the 9-ball to be transferred to the 13-ball.
d) In this collision, momentum is not conserved.
This statement is not true because in an elastic collision, momentum is always conserved. The total momentum before the collision should be equal to the total momentum after the collision.
e) In this collision energy, is not conserved.
This statement is not true because in an elastic collision, energy is always conserved. The total kinetic energy before the collision should be equal to the total kinetic energy after the collision.
Based on the analysis, the best choice (given options a to e) is b) All of the 9-ball’s energy and some of its momentum are transferred to the 13-ball. This choice aligns with the principles of an elastic collision, where both energy and momentum are conserved.