The force sensor measures the force on the sensor due to the bumper, but the cart's momentum change arises from the force on the cart due to the bumper. Which of the following facts are needed to assert that the magnitude of these two forces are nearly equal at all times.
A. Their magnitudes differ by the magnitude of the net force on the bumper.
B. The force of friction is small.
C. The net force on the bumper is small.
D. The cart's weight is canceled by the the normal force exerted by the track.
1. A, B
2. A, C
3. A, D
4. B, C
5. B, D
6. C, D
7. A, B, C, D
To determine which of the facts are needed to assert that the magnitude of the force on the force sensor and the force on the cart due to the bumper are nearly equal at all times, we can analyze each fact individually:
A. Their magnitudes differ by the magnitude of the net force on the bumper.
This fact is essential because it implies that the force on the force sensor and the force on the cart due to the bumper are influenced by the same net force. If their magnitudes differ by the magnitude of the net force on the bumper, then they will be nearly equal.
B. The force of friction is small.
The force of friction is not directly related to the assertion about the magnitudes of the forces on the force sensor and the cart due to the bumper. So, this fact is not needed to assert the near equality of the two forces.
C. The net force on the bumper is small.
This fact is important because if the net force on the bumper is small, then the force on the force sensor and the force on the cart due to the bumper will be comparable in magnitude. So, this fact is needed to assert the near equality of the two forces.
D. The cart's weight is canceled by the normal force exerted by the track.
This fact is also crucial because the weight of the cart is balanced by the normal force exerted by the track, implying that there are no additional forces that would significantly affect the magnitudes of the forces on the force sensor and the cart due to the bumper. Therefore, this fact is needed to assert the near equality of the two forces.
Based on this analysis, the correct answer is:
7. A, B, C, D, which means that all the facts are needed to assert that the magnitude of the forces on the force sensor and the cart due to the bumper are nearly equal at all times.