Question

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: 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 interval \(\Delta t\) is the same for all chairs (since the problem is about the relationship between force, mass, and change in speed, and no information about time difference is given), we can compare forces based on \(F = m\Delta v\) (because \(a=\frac{\Delta v}{\Delta t}\) and \(\Delta t\) is constant).

Step2: Analyze each option

• Option a:

The blue and red chairs have more mass (\(m_{blue}=m_{red}>m_{yellow}\)) and \(\Delta v\) (change in speed). For the yellow chair, \(\Delta v = 2m/s\) (assuming initial speed \(0\) as it's a common - starting - point assumption for such problems, but even if not, the formula \(F = m\Delta v\) holds). For the blue and red chairs, if we assume the blue chair's speed change (say from \(v_1\) to \(v_2\)) and red chair's speed change (from \(v_3\) to \(v_4\)) and yellow chair's speed change (from \(v_5\) to \(v_6\)). Using \(F = m\Delta v\), since \(m_{blue}=m_{red}>m_{yellow}\) and if we assume \(\Delta v\) (after proper calculation of speed - change, for example, if the blue chair's speed change is non - zero and comparable in magnitude to the red chair's speed change in a way that \(m_{blue}\Delta v_{blue}=m_{red}\Delta v_{red}>m_{yellow}\Delta v_{yellow}\)).

• Option b:

Force is not about the final speed (\(v_f\)) but about the change in speed (\(\Delta v=v_f - v_i\)). So, just having a high final speed does not imply a large force. Using \(F = ma=m\frac{\Delta v}{\Delta t}\), final speed alone is not a determinant of force.

• Option c:

Since \(m_{blue}=m_{red}>m_{yellow}\) and \(F = m\Delta v\) (with \(\Delta t\) constant), if \(\Delta v\) were the same for all (which is not the case as we can calculate speed - changes: for example, if we assume initial speeds. Let's say the blue chair's speed change: if it was moving at some initial speed and then had a change. The yellow chair has a speed of \(2m/s\) (assuming from rest, \(\Delta v = 2m/s\)), and for the blue and red chairs, their speed - changes (calculated as \(v_{final}-v_{initial}\)) when multiplied by their larger masses will give a larger force. So, they do not experience the same force.

• Option d:

The direction of speed change (speeding up or slowing down) does not affect the magnitude of the force in the formula \(F = ma=m\frac{\Delta v}{\Delta t}\). The magnitude of \(\Delta v\) (the change in speed, regardless of whether it's an increase or decrease) and mass are the factors.

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.