Question

1. three friends were kicking soccer balls at a neighborhood field. three soccer balls were rolling across the field. the black soccer ball has less mass than the blue and orange balls, which have equal mass. all three soccer balls were kicked by one of the friends, but not all from the same direction. use the information in the diagram to answer. which soccer ball(s) experienced the strongest force? how do you know?

a all three soccer balls experienced the same force because they changed speed by the same amount.
b the orange soccer ball; it has more mass and the fastest ending speed.
c the blue soccer ball; it takes a stronger force to slow down a more massive object than to speed it up.
d the blue and orange soccer balls; they have more mass than the black soccer ball, but changed speed by the same amount

Explanation:

Step1: Recall Newton's second law

According to Newton's second law \(F = ma\) (where \(F\) is force, \(m\) is mass, and \(a\) is acceleration). Acceleration \(a=\frac{\Delta v}{\Delta t}\) (change in velocity over change in time). If the change in velocity (\(\Delta v\)) is the same (assuming the time of interaction \(\Delta t\) is the same, which is a reasonable assumption for a kick - like interaction), then \(F\propto m\) (force is proportional to mass).

Step2: Analyze each option

• Option a: If all three balls had the same force, then \(a=\frac{F}{m}\). Since the masses are different (\(m_{black}
• Option b: The orange ball has the same mass as the blue ball. If we assume the kick imparts a force related to the change in speed. But there is no information to suggest that the orange ball has the fastest - ending speed implies the strongest force. In fact, from \(F = ma\), if we consider the change in speed (acceleration) and mass. Since the blue and orange have the same mass, and if we assume the same change in speed (a reasonable assumption for a similar interaction like a kick), they should have the same force.
• Option c: The blue ball (and orange ball, since \(m_{blue}=m_{orange}\)) has more mass than the black ball. According to \(F = ma\), for the same change in speed (acceleration), a more massive object requires a stronger force. But the problem is asking which ball experienced the strongest force. If we assume the same change in speed (a common assumption for a kick - like impulse), then the blue and orange (with higher mass) would have a stronger force. But this option is incorrect because it mis - relates the force for speeding up and slowing down in a non - physical way for this context (a kick is an impulsive force that changes the motion, not just slowing down).
• Option d: Since \(m_{blue}=m_{orange}\) and assuming the same change in speed (a reasonable assumption for a kick, as the interaction (kick) is a similar impulse - like event), using \(F = ma\) (where \(a=\frac{\Delta v}{\Delta t}\), and \(\Delta t\) is the same for the kick), the force on the blue and orange balls is the same.

Answer:

d. The blue and orange soccer balls; they have more mass than the black soccer ball, but changed speed by the same amount.