How Does Physics Explain a Ball Shot from a Spring into a Ballast?

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The discussion revolves around calculating the dynamics of a ball shot from a spring into a ballast. To determine the speed of the ballast-ball system immediately after impact, conservation of momentum principles are applied. The speed of the ball before impact is calculated using the same momentum conservation principles. Additionally, the spring's compression needed to achieve the ball's speed is found through conservation of energy. These calculations highlight the interplay of kinetic energy, potential energy, and momentum in this physics scenario.
twjtiger
This question is blowing my mind, can anyone help?

A ball is shot out of a projector by a spring and into a hollow ballast which then swings upwards 2.5 cm. The ball has a mass of 0.10 kg, the ballast has a mass of 0.50 kg, and the spring constant is 500 N/m.

a. How fast is the ballast-ball system moving immediately after impact?

b. How fast was the ball moving immediately before impact?

c. How far was the spring compressed in order to release the ball with this speed?
 
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Use conservation of energy for (a) and (c), and linear momentum conservation for (b).
 

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