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