Question

Critical Thinking Two boxes of equal mass slide start from rest and slide with different horizontal applied forces across frictionless surfaces to reach the same distance away. Box A has a horizontal force of three times that of box B. (a) Which box is traveling faster at this distance away from the starting point? Briefly explain your reasoning. (b) Based on experimental data, an equation that fits the data is suggested for the final speed, V, which may not be correct: V=KF, where K is a constant with appropriate units and F is the horizontal applied force. Is this equation consistent with your answer from part a? Explain why or why not. Does this equation make sense? Explain why or why not. (c) Now the applied force can be any value and the distance from the starting point is measured when the speed gets to a consistent value. Graph the distance the box gets to at a given speed as a function of the applied force.Which box is traveling faster at this distance away from the starting point? Briefly explain your reasoning.

A. Box A
B. Box B
C. Both boxes are traveling at the same speed
D. Cannot be determined with given information

Answer 1

Box A is traveling faster at the finishing distance due to a greater applied force and resulting acceleration. The equation V = KF is consistent with part (a) and makes sense as it represents the relationship between the final speed and applied force. The box with a greater applied force will generally travel faster at the same distance from the starting point.

Step-by-step explanation:

(a) Box A travels faster at the finishing distance since a greater force with equal mass results in a greater acceleration. Also, a greater acceleration over the same distance results in a greater final speed.

(b) The equation V = KF is consistent with the answer from part (a). Since V represents the final speed, which is the same as the speed at the finishing distance, and F represents the applied force, the equation indicates that as the force increases, the final speed also increases.

(c) The graph of the distance the box gets to at a given speed as a function of the applied force will depend on the specific values of forces and speeds chosen. However, the box with a greater applied force will generally travel faster at the same distance from the starting point, as explained in part (a).