Ball compressing spring

In summary, a ball with a mass of 0.25 kg is shot into the barrel of a spring gun with a velocity of 120 m/s. The spring gun has a mass of 1.8 kg and is initially at rest on a frictionless surface. The ball gets stuck in the barrel at the point of maximum compression of the spring. With no energy lost to friction, it is asked what fraction of the ball's initial kinetic energy is stored in the spring. The solution involves using the conservation of momentum in an inelastic collision and translating it into a center of mass reference frame. By finding the kinetic energy of the center of mass of the system before the collision, the amount of energy lost into internal spring potential can be
  • #1
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A ball of mass 0.25 kg is fired with velocity 120 m/s into the barrel of a spring gun of mass 1.8 kg initially at rest on a frictionless surface. The ball sticks in the barrel at the point of maximum compression of the spring. No energy is lost to friction. What fraction of the ball's initial kinetic energy is stored in the spring?
 
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  • #2
You'll need inelastic collision conservation of momentum:
(m1+m2)V_cen. of mass = m1v1 +m2v2

And a translation into a center of mass reference frame:
v'1 + v_cen. of mass = v1

If you get the kinetic energy of the center of mass of the system before the collision that will be the kinetic energy that was lost into internal spring potential...

Maybe there is an easier way, but I'm pretty sure this will get you the answer.
 

1. What is a ball compressing spring?

A ball compressing spring is a type of mechanical spring that is designed to compress or exert force on a ball or spherical object. It is typically made of metal and is used to store and release energy in a controlled manner.

2. How does a ball compressing spring work?

A ball compressing spring works by using the mechanical principle of elasticity. When a force is applied to the spring, it compresses or shortens, storing potential energy. When the force is released, the spring expands, releasing the stored energy.

3. What are the applications of ball compressing springs?

Ball compressing springs have a wide range of applications in various industries. They are commonly used in ball valves, automotive engines, and shock absorbers. They can also be found in toys, exercise equipment, and mechanical devices.

4. How do I choose the right ball compressing spring for my application?

The right ball compressing spring for your application will depend on factors such as the required force, deflection, and space constraints. You should also consider the material, size, and shape of the spring. It is best to consult with a spring manufacturer for guidance on selecting the right spring for your specific needs.

5. How do I maintain and prolong the lifespan of a ball compressing spring?

To maintain and prolong the lifespan of a ball compressing spring, it is important to avoid overloading or compressing it beyond its designed limits. Regularly inspect the spring for any signs of wear or damage and replace it if necessary. Proper storage and handling can also help to extend the lifespan of the spring.

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