Question

Two bowling balls of different masses collide while accelerating at 1.875 m/s 2
. 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?(1 point)
Responses

8.875 N to the right
8.875 N to the right

7.5 N to the left
7.5 N to the left

13.125 N to the right
13.125 N to the right

3.73 N to the right

Answer 1

To find the force that the 7 kg bowling ball (Ball A) exerts on the 4 kg bowling ball (Ball B), we can use Newton's second law of motion, which states that \( F = ma \), where \( F \) is the force, \( m \) is the mass, and \( a \) is the acceleration.

Given that both balls are experiencing the same acceleration of \( a = 1.875 \, \text{m/s}^2 \):

1. For Ball A (7 kg):
\[
F_A = m_A \cdot a = 7 \, \text{kg} \cdot 1.875 \, \text{m/s}^2 = 13.125 \, \text{N}
\]

2. For Ball B (4 kg):
\[
F_B = m_B \cdot a = 4 \, \text{kg} \cdot 1.875 \, \text{m/s}^2 = 7.5 \, \text{N}
\]

However, the force that Ball A exerts on Ball B will be equal in magnitude but opposite in direction to the force that Ball B exerts on Ball A, as per Newton's third law of motion.

Since both balls are accelerating in the same direction (to the right for the 7 kg ball and to the left for the 4 kg ball), and we want to find the force exerted by Ball A on Ball B (which is in the direction of Ball B’s acceleration), we have:

- The force exerted by Ball A on Ball B is \( 13.125 \, \text{N} \) and since Ball A is rolling to the right, this force is directed to the right.

Thus, the correct response is:

**13.125 N to the right**