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

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SUMMARY

The discussion focuses on the physics principles governing the motion of a ball shot from a spring into a ballast. The ball, with a mass of 0.10 kg, is propelled by a spring with a constant of 500 N/m into a ballast of 0.50 kg, which swings upwards by 2.5 cm after impact. The calculations involve using conservation of energy to determine the speed of the ballast-ball system immediately after impact and the compression of the spring, while linear momentum conservation is applied to find the ball's speed just before impact.

PREREQUISITES
  • Understanding of conservation of energy principles
  • Knowledge of linear momentum conservation
  • Familiarity with spring mechanics and Hooke's Law
  • Basic physics concepts related to mass and velocity
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  • Calculate the initial velocity of the ball using conservation of energy equations
  • Explore the concept of momentum conservation in elastic collisions
  • Investigate the relationship between spring compression and potential energy
  • Review examples of similar physics problems involving springs and projectiles
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Students studying physics, educators teaching mechanics, and anyone interested in understanding the dynamics of spring-loaded projectiles and their interactions with other masses.

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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