Question

1. kristina has three skateboards for her skateboarding competitions. the brown and pink skateboards are of equal mass and more massive than the green skateboard, which has the least mass. one day, she tested the skateboards by giving each a push, but not from the same direction. use the information in the diagram to answer.

which skateboard(s) experienced the strongest force from kristinas push? how do you know?
a. the pink skateboard experienced the strongest force for two reasons: it is a more massive object and it has the fastest ending speed.
b. the brown skateboard experienced the strongest force because it requires more force to slow an object down than to speed it up.
c. the brown and pink skateboards experienced the strongest force because they are both more massive than the green skateboard and they changed speed by the same amount.
d. all three skateboards experienced the same strength force because they changed speed by the same amount.

Explanation:

Step1: Recall Newton's second law

Newton's second law is \(F = ma\), where \(F\) is force, \(m\) is mass, and \(a\) is acceleration. Acceleration \(a=\frac{\Delta v}{\Delta t}\). Assuming the time of the push \(\Delta t\) is the same for all skate - boards (since the problem is about comparing forces based on mass and speed - change), we can compare \(F\propto m\Delta v\).

Step2: Calculate \(m\Delta v\) for each skateboard

• Brown skateboard: \(m = 2.2\space kg\), \(\Delta v=\vert3 - 10\vert= 7\space m/s\), so \(m\Delta v=2.2\times7 = 15.4\space kg\cdot m/s\)
• Pink skateboard: \(m = 2.2\space kg\), \(\Delta v=14 - 7=7\space m/s\), so \(m\Delta v=2.2\times7 = 15.4\space kg\cdot m/s\)
• Green skateboard: \(m = 1.6\space kg\), \(\Delta v=20 - 13 = 7\space m/s\), so \(m\Delta v=1.6\times7=11.2\space kg\cdot m/s\)

The brown and pink skateboards have the same \(m\Delta v\) (since they have the same mass and same \(\Delta v\)), and both \(m\Delta v\) values for brown and pink are greater than that of the green skateboard.

Answer:

C. The brown and pink skateboards experienced the strongest force because they are both more massive than the green skateboard and they changed speed by the same amount.