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Answer :
Final answer:
The spring compresses by approximately 0.108 meters in bringing the ball to a stop.
Explanation:
To find the distance the spring compresses in bringing the ball to a stop, we can use the principle of conservation of energy. When the ball stops, all of its kinetic energy is converted into potential energy stored in the compressed spring. The potential energy stored in a spring is given by the equation:
PE = 1/2 k x²
where PE is the potential energy, k is the spring constant, and x is the displacement of the spring. We can rearrange the equation to solve for x:
x = sqrt(2 PE / k)
Substituting the values given in the question, we have:
x = sqrt(2 * (0.5 * 0.103 kg * (11.9 m/s)²) / 66.9 N/m) = 0.108 m
Therefore, the spring compresses by approximately 0.108 meters in bringing the ball to a stop.
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