Question

force and motion end - of - unit assessment (continued)

1. three chairs were rolling across a flat office floor. the blue and red chairs are the same mass, and they have more mass than the yellow chair. each chair was hit by another chair, but not from the same direction. use the information in the diagram to answer.

which chair(s) experienced the strongest force when hit? how do you know?

a. the blue and red chairs experienced the strongest force because they are both more massive than the yellow chair and they changed speed by the same amount.
b. the red chair experienced the strongest force because it is as massive as the blue chair and has the highest ending speed.
c. all three chairs experienced the same force because they changed speed by the same amount.
d. the blue chair experienced the strongest force because it takes more force to slow an object than it takes to make it go faster.

Explanation:

Step1: Calculate the force for each chair

According to Newton's second law \(F = ma\), and \(a=\frac{\Delta v}{\Delta t}\). Assuming the time \(\Delta t\) is the same for all chairs (since the problem doesn't mention different - time intervals for the force application), we can compare \(F\) by comparing \(m\Delta v\).

• For the blue chair: \(m = 12\space kg\), \(\Delta v=1 - 4=- 3\space m/s\), so \(m\Delta v=12\times(-3)=- 36\space kg\cdot m/s\) (magnitude is \(36\space kg\cdot m/s\))
• For the red chair: \(m = 12\space kg\), \(\Delta v=6 - 3 = 3\space m/s\), so \(m\Delta v=12\times3 = 36\space kg\cdot m/s\)
• For the yellow chair: \(m = 10\space kg\), \(\Delta v=5 - 2=3\space m/s\), so \(m\Delta v=10\times3 = 30\space kg\cdot m/s\)

Step2: Compare the magnitudes of \(m\Delta v\)

Since \(F\propto m\Delta v\) (when \(\Delta t\) is constant), and \(36>30\)

Answer:

A. The blue and red chairs experienced the strongest force because they are both more massive than the yellow chair and they changed speed by the same amount.