Question

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? before black soccer ball: 25 kg (less mass) speed: 7 m/s blue soccer ball: 43 kg (more mass) speed: 18 m/s orange soccer ball: 43 kg (more mass) speed: 25 m/s after speed: 25 m/s speed up by 18 m/s speed: 4 m/s slowed down by 14 m/s speed: 29 m/s sped up by 4 m/s all three soccer balls experienced the same force because they changed speed by the same amount. the orange soccer ball; it has more mass and the fastest ending speed. the blue soccer ball; it takes a stronger force to slow down a more massive object than to speed it up. the blue and orange soccer balls; they have more mass than the black soccer ball, but changed speed by the same amount. this is a required question

Explanation:

Step1: Recall Newton's second law

Force $F = ma$, where $m$ is mass and $a$ is acceleration. Acceleration $a=\frac{\Delta v}{\Delta t}$. Assuming the time - interval $\Delta t$ is the same for all balls, we can compare forces by looking at mass $m$ and change in velocity $\Delta v$.

Step2: Analyze the change in velocity of each ball

The black ball: Initial speed $v_{i1}=7$ m/s, final speed $v_{f1}=34$ m/s, $\Delta v_1=34 - 7=27$ m/s, mass $m_1 = 0.25$ kg.
The blue ball: Initial speed $v_{i2}=18$ m/s, final speed $v_{f2}=4$ m/s, $\Delta v_2=4 - 18=- 14$ m/s, mass $m_2 = 0.43$ kg.
The orange ball: Initial speed $v_{i3}=25$ m/s, final speed $v_{f3}=52$ m/s, $\Delta v_3=52 - 25 = 27$ m/s, mass $m_3 = 0.43$ kg.

Step3: Calculate the force magnitude for each ball (ignoring the sign of acceleration for force - magnitude comparison)

For the black ball, $F_1=m_1a_1=m_1\frac{\Delta v_1}{\Delta t}=0.25\times\frac{27}{\Delta t}=\frac{6.75}{\Delta t}$.
For the blue ball, $F_2=m_2a_2=m_2\frac{|\Delta v_2|}{\Delta t}=0.43\times\frac{14}{\Delta t}=\frac{6.02}{\Delta t}$.
For the orange ball, $F_3=m_3a_3=m_3\frac{\Delta v_3}{\Delta t}=0.43\times\frac{27}{\Delta t}=\frac{11.61}{\Delta t}$.

Since the orange and blue balls have more mass than the black ball and the orange ball has a large positive change in velocity and the blue ball has a negative change in velocity, and comparing the magnitudes of the forces calculated from $F = ma$, the orange ball experiences the strongest force because it has more mass and a large change in velocity.

Answer:

The orange soccer ball; it has more mass and the fastest ending speed.