Two bowling balls of different masses collide while accelerating at 1.875 m/s2

. The first ball, rolling to the right, weighs 7 kg. The second ball, rolling to the left, weighs 4 kg. What force does the bowling ball weighing 7 kg exert on the bowling ball weighing 4 kg?
Responses

13.125 N to the right
13.125 N to the right - no response given

3.73 N to the right
3.73 N to the right - no response given

8.875 N to the right
8.875 N to the right - no response given

7.5 N to the left

1 answer

To determine the force exerted by the 7 kg bowling ball on the 4 kg bowling ball, we first need to calculate the net force acting on each of the balls due to their acceleration. According to Newton's second law:

\[ F = m \cdot a \]

where \( F \) is the force, \( m \) is the mass, and \( a \) is the acceleration.

For the 7 kg bowling ball:

\[ F_1 = m_1 \cdot a = 7 , \text{kg} \cdot 1.875 , \text{m/s}^2 = 13.125 , \text{N} \]

This force is directed to the right, since the ball is moving to the right.

For the 4 kg bowling ball:

\[ F_2 = m_2 \cdot a = 4 , \text{kg} \cdot 1.875 , \text{m/s}^2 = 7.5 , \text{N} \]

This force would also be directed to the right but is actually required to maintain its leftward motion as it collides with the first ball.

According to Newton's third law, the force exerted by the 7 kg ball on the 4 kg ball will be equal in magnitude and opposite in direction to the force exerted by the 4 kg ball on the 7 kg ball.

Therefore, the force exerted by the 7 kg bowling ball on the 4 kg bowling ball is:

13.125 N directed to the left (because the 7 kg ball is influenced to the right).

Consequently, none of the provided responses accurately reflects the force exerted by the 7 kg bowling ball on the 4 kg bowling ball in the correct direction. However, the calculation shows the magnitude is correct:

13.125 N to the left.