When the student throws the two balls with the same amount of force, the acceleration of each ball can be determined using Newton's second law of motion, which states that \( F = ma \) (force equals mass times acceleration).
Rearranging this formula gives us \( a = \frac{F}{m} \), where \( a \) is acceleration, \( F \) is the force applied, and \( m \) is the mass of the object.
Let's assume the force exerted by the student is \( F \).
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For the first ball (0.25 kg): \[ a_1 = \frac{F}{0.25} \]
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For the second ball (0.5 kg): \[ a_2 = \frac{F}{0.5} \]
Since both balls are thrown with the same force \( F \), the accelerations can be analyzed:
- The first ball (0.25 kg) will have a greater acceleration because its mass is smaller. If you plug values in, you can see how the accelerations compare:
- For the first ball: \( a_1 = \frac{F}{0.25} = 4F \)
- For the second ball: \( a_2 = \frac{F}{0.5} = 2F \)
Thus, the acceleration of the first ball (0.25 kg) will be greater than that of the second ball (0.5 kg). This happens because, for a given force, a lighter object will accelerate more than a heavier object. In summary:
- The ball with a mass of 0.25 kg will experience greater acceleration compared to the ball with a mass of 0.5 kg due to having the same force applied to each, as acceleration is inversely proportional to mass.
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