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In which of the following situations will a ball experience the greatest acceleration?

Rationale

A 200 Newton force is applied to a 50 g ball.

Acceleration is calculated using Newton's second law, \( a = \frac{F}{m} \). Here, the force applied and the mass of the ball determine the acceleration; the smaller the mass with a given force, the greater the acceleration experienced.

A (A 100 Newton force is applied to a 100 g ball.) YOUR ANSWER

Applying a 100 Newton force to a 100 g ball results in an acceleration of \( a = \frac{100 \, \text{N}}{0.1 \, \text{kg}} = 1000 \, \text{m/s}^2 \). While this is considerable, it is not the highest compared to the other scenarios presented.

B (A 100 Newton force is applied to a 175 kg ball.) YOUR ANSWER

In this case, the acceleration is calculated as \( a = \frac{100 \, \text{N}}{175 \, \text{kg}} \approx 0.57 \, \text{m/s}^2 \). Due to the significantly larger mass, the acceleration is quite low, making this option the least favorable for experiencing high acceleration.

C (A 200 Newton force is applied to a 250 g ball.) YOUR ANSWER

This scenario yields an acceleration of \( a = \frac{200 \, \text{N}}{0.25 \, \text{kg}} = 800 \, \text{m/s}^2 \). While this value is high, it is still lower than the acceleration experienced by the ball in option D.

D (A 200 Newton force is applied to a 50 g ball.) CORRECT

Here, the acceleration is calculated as \( a = \frac{200 \, \text{N}}{0.05 \, \text{kg}} = 4000 \, \text{m/s}^2 \). This is the highest acceleration among all options, clearly illustrating that the combination of a large force and a small mass results in maximum acceleration.

Conclusion

The situation where a 200 Newton force is applied to a 50 g ball produces the greatest acceleration, calculated at 4000 m/s². This is due to the minimal mass of the ball allowing for a large acceleration when subjected to a significant force. Other options present higher masses or lower forces, resulting in comparatively lower accelerations.

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