Question

imagine you are in a bumper car and you bump into someone with less mass than you do. in this scenario, you bounce back just a little bit, but the other person goes zooming across the floor. is it true or false that the forces you experience during the collision are the same? true false

Explanation:

Step1: Apply Newton's Third Law

According to Newton's Third Law of Motion, for every action, there is an equal and opposite reaction. When two bumper - cars collide, the force exerted by your car on the other car (\(F_{1}\)) and the force exerted by the other car on your car (\(F_{2}\)) are a pair of action - reaction forces.

Mathematically, \(F_{1}=-F_{2}\), which means the magnitudes of the forces are equal (\(\vert F_{1}\vert=\vert F_{2}\vert\)) and the directions are opposite.

Step2: Consider the effect of mass on motion

The difference in motion (you bounce back a little bit and the other person zooms across the floor) is due to Newton's Second Law \(F = ma\) (where \(F\) is force, \(m\) is mass, and \(a\) is acceleration). Since \(F\) (the magnitude of the force) is the same for both cars during the collision (from Step 1), but the masses (\(m\)) are different.

If \(m_{1}>m_{2}\) (your car has a larger mass \(m_{1}\) and the other car has a smaller mass \(m_{2}\)), then from \(a=\frac{F}{m}\), the acceleration of the car with smaller mass (\(a_{2}=\frac{F}{m_{2}}\)) is larger than the acceleration of the car with larger mass (\(a_{1}=\frac{F}{m_{1}}\)) because \(\frac{F}{m_{2}}>\frac{F}{m_{1}}\) when \(m_{2}

Answer:

A. True