Chapter 3, Problem 32P

Students Lucia. Isabel, and Austin are investigating how snow stops a dropped 500-g lemon juice bottle. In particular, they are interested in how the force exerted by the snow depends on the age of the snow. They take high-speed videos of the bottle while it sinks into the snow, taking their first set of measurements 4 days after fresh snowfall and the second set of measurements 2 days later. After analyzing the videos frame by frame (see photo), they plot a graph that shows how the velocity of the bottle from the moment the bottle touches the snow changes for both types of snow (Figure P3.32

They each explain their results as follows:

Lucia The 6-day snow exerts a larger force on the bottle because it stops the bottle in a shorter time.

Isabel The time taken to stop the bottle does not say much about the force. The 6-day snow exerts a larger force on the bottle because the slope of its v_v (t) graph is steeper.

Austin We cannot compare the forces exerted by the snow because the initial velocities are different. We need to repeat the experiments and make sure we always drop the bottle from the same height

Explain how each student reached her/his conclusion and decide who (if anyone) is correct indicate any assumptions that you have made.