Question

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? the blue chair experienced the strongest force because it takes more force to slow an object than it takes to make it the red chair experienced the strongest force because it is as massive as the blue chair and has the highest ending speed. 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. all three chairs experienced the same 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 is the change in velocity (\(\Delta v\)) over time (\(t\)), \(a=\frac{\Delta v}{t}\). If the time of interaction (when hit) is the same for all chairs, we can compare forces based on mass and \(\Delta v\).

Step2: Analyze the mass - acceleration relationship

The blue and red chairs have the same mass (\(m_{blue}=m_{red}\)) and more mass than the yellow chair (\(m_{blue}=m_{red}>m_{yellow}\)). From the diagram (assuming the change in speed \(\Delta v\) is the same for blue and red chairs, and different for yellow, but if we consider the fact that for objects with non - zero mass, and using \(F = m\times\frac{\Delta v}{t}\). If \(\frac{\Delta v}{t}\) (rate of change of velocity) is the same (as per the problem's implication from the “hit” situation, assuming same time of force application and same change in motion pattern for blue and red), then \(F\propto m\) (force is proportional to mass).

Answer:

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.