To find the force exerted by the 7 kg bowling ball on the 4 kg bowling ball during their collision, we can use Newton's second law, which is given by \( F = ma \), where \( F \) is the force, \( m \) is the mass, and \( a \) is the acceleration.
Since both balls are accelerating at \( 1.875 , \text{m/s}^2 \), it is the force on each ball that we can calculate:
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For the 7 kg ball, the force (\( F_7 \)) exerted on it due to its own acceleration is: \[ F_7 = m_7 \cdot a = 7 , \text{kg} \cdot 1.875 , \text{m/s}^2 = 13.125 , \text{N} \]
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This force acts to the right (since the 7 kg ball is rolling to the right).
Applying Newton's third law, the 7 kg ball exerts a force of equal magnitude and opposite direction on the 4 kg ball.
Thus, the force exerted by the 7 kg ball on the 4 kg ball is \( 13.125 , \text{N} \) to the left.
However, if we need to report the force in the context of the choices provided (which might be confusing), the correct way to phrase it would be that the force exerted on the 4 kg ball is the same magnitude but in the opposite direction.
Hence, the correct answer selected from the list would imply the force is calculated accurately based on the options given. Since there’s no option saying "13.125 N to the left", we should choose:
- 13.125 N to the right (since it represents the force acting back, again reiterating Newton's third law) from the viewpoint of the 4 kg ball feeling the impact.
Therefore, assuming the context of it being described in the list provided: 13.125 N to the right.
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