Question

1. alfonso, julia, and margie were having fun as they rolled some office chairs across a flat floor. all three chairs have the same mass. margie gave each of the chairs a push, but not all from the same direction. each chair changed speed as a result of being pushed. use the information in the diagram to answer. which chair(s) experienced the strongest force when it was pushed? how do you know? a the black chair experienced the strongest force because it takes a stronger force to slow something down than it takes to speed something up. b the blue chair experienced the strongest force because it had the fastest ending speed. c all three chairs experienced the same strength force because they changed speed by the same amount. d the pink and blue chairs experienced the strongest forces because they both gained the same force as they sped up. the black chair lost force, so it slowed down.

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 \(a=\frac{\Delta v}{\Delta t}\). Here, assume the time of pushing \(\Delta t\) is the same for all chairs (since Margie gives a push - a short - time interaction). The mass \(m\) of the chairs is the same.

Step2: Analyze the change in velocity (\(\Delta v\))

The change in velocity \(\Delta v=v_{final}-v_{initial}\). For the black chair: if we assume initial speed \(v_{i}\) and final speed \(v_{f}\), \(\vert\Delta v\vert=\vert v_{f}-v_{i}\vert\). For the pink and blue chairs, \(\Delta v = v_{f}-v_{i}\) (positive as they speed up). If we calculate the magnitude of \(\Delta v\) (since acceleration \(a\propto\Delta v\) when \(\Delta t\) is constant) for all three chairs, we find that \(\vert\Delta v_{black}\vert=\vert\Delta v_{pink}\vert=\vert\Delta v_{blue}\vert\).
Since \(F = ma\) and \(m\) is the same and \(a\propto\Delta v\) (for constant \(\Delta t\)), the force \(F\) is the same for all chairs.

Answer:

C. All three chairs experienced the same strength force because they changed speed by the same amount.