Question

Critical Thinking Two boxes of the same mass are pressed against pistons that compress and release the boxes on frictionless surfaces. Box A’s piston has a constant force F over a distance x before the box is released while box B starts at zero force and increases linearly to a force of 2F before releasing the box at a distance of 1/2d. (a) Which of these boxes has the greatest speed after releasing from the piston? (b) Based on experimental data for trials similar to box A, an equation that fits the data is suggested for the change in kinetic energy, ΔKE, which may not be correct: ΔKE=KF1/2x1/2, where K is a constant with appropriate units, F is the applied force, and x is the distance the piston moves in contact with the box. 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) If the applied force of the piston is proportional to the distance in contact with the box, graph the work done on the box vs. the distance in contact with the piston and box.(a) Which of these boxes has the greatest speed after releasing from the piston?

A. Box A
B. Box B
C. Both have the same speed
D. It depends on additional factors

Answer 1

Box B has the greatest speed after releasing from the piston. The equation ΔKE = KF1/2x1/2 is not consistent with the answer from part a. If the applied force of the piston is proportional to the distance in contact with the box, the graph of work done on the box vs. the distance in contact will be linear.

Step-by-step explanation:

a) Box B

Box B will have the greatest speed after releasing from the piston because it experiences an increasing force over a shorter distance compared to Box A. The force acting on Box B increases linearly from zero to 2F, while Box A experiences a constant force F over a distance x.

b) No

The equation for change in kinetic energy, ΔKE = KF1/2x1/2, is not consistent with the answer from part a. The equation does not take into account the difference in forces and distances between Box A and Box B, and it does not accurately represent the relationship between force, distance, and kinetic energy.

c) Work done vs. distance

If the applied force of the piston is proportional to the distance in contact with the box, the graph of work done on the box vs. the distance in contact with the piston and box will be a linear relationship. As the distance in contact increases, the work done also increases proportionally.