Question

force and motion end - of - unit assessment
multiple - choice questions

1. three toy boats with the same mass were in a lake. two boats were moving and one was stopped. each boat got bumped by another boat, but not in the same direction. all the boats changed speed as a result of being bumped. use the information in the diagram to answer.

which toy boat(s) experienced the strongest force when it was bumped? how do you know?
a. the blue toy boat experienced the strongest force because it takes a stronger force to slow something down than it takes to speed something up.
b. the gray toy boat experienced the strongest force because it had the fastest ending speed.
c. the orange and gray toy boats experienced the strongest forces because they both gained the same force as they sped up. the blue boat lost force, so it slowed down.
d. all three toy boats 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 bump (\(\Delta t\)) is the same for all boats.

Step2: Calculate the change in velocity (\(\Delta v\)) for each boat

• For the blue boat: \(\Delta v=3 - 8=- 5\space km/h\) (magnitude of change in velocity \(|\Delta v| = 5\space km/h\))
• For the orange boat: \(\Delta v=5 - 0 = 5\space km/h\)
• For the gray boat: \(\Delta v=17 - 12=5\space km/h\)

Since \(F = ma\) and \(m\) (mass) is the same for all boats (given in the problem) and assuming \(\Delta t\) (time of interaction) is the same (not stated otherwise, a reasonable assumption for a bump - like interaction), and \(a=\frac{\Delta v}{\Delta t}\), the force \(F\) is proportional to \(\Delta v\) (because \(F=m\frac{\Delta v}{\Delta t}\)).

Answer:

d. All three toy boats experienced the same strength force because they changed speed by the same amount.