Maximum Compression of a Spring in a Collision?

In summary, the conversation discusses how to calculate the maximum compression of a spring after a perfectly inelastic collision with a wall. The participants consider using Newton's Third Law, conservation of momentum, and physical intuition to solve the problem. Ultimately, they determine that conservation of energy can be used to solve for the maximum compression, with the equation mv²=kx².
  • #1
planck42
82
0

Homework Statement


An object with mass m is being held on a spring in equilibrium position with spring constant k. This system(both the object and the spring) is moving in one direction with a velocity v. The system then collides perfectly inelastically with a wall. What is the maximum compression of the spring?

Homework Equations


F=-kx
Conservation of Momentum(?)
Newton's Third Law of Motion

The Attempt at a Solution


By Newton's Third Law, the force the wall exerts on the system is equivalent in magnitude to the force the system pushes on the wall. However, the force appears incalculable. Newton's Second Law cannot really be used here because it concerns net force on an object. Therefore, it appears that the only way out is to calculate the impulse the object is experiencing and then to take the time derivative of that impulse. This does not seem to accomplish anything either, since the impulse is mv, and when one takes the time derivative of that, it comes out to be ma, which doesn't help my cause one bit. I feel at an impasse with this problem. Help would be much appreciated.
 
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  • #2
Perhaps we can use some physical intuition to find a relevant equation.

Perfectly inelastic generally means the two objects "stick" together and for most situations means that you can't rely on conservation of energy. However, in this case you could argue that the energy is completely converted into potential energy of the spring and hence we could try using conservation of energy.

With this tool at your hands, the solution is simple.
 
  • #3
Coto said:
Perhaps we can use some physical intuition to find a relevant equation.

Perfectly inelastic generally means the two objects "stick" together and for most situations means that you can't rely on conservation of energy. However, in this case you could argue that the energy is completely converted into potential energy of the spring and hence we could try using conservation of energy.

With this tool at your hands, the solution is simple.

Ah! I never thought of it that way. So what you're saying is that mv²=kx² since the 1/2's cancel.
 
  • #4
Correct. All you need to do is isolate for x then.
 

1. What is the force of a collision?

The force of a collision is the amount of energy that is transferred during a collision. It is a measure of how much two objects push or pull on each other when they come into contact.

2. How is the force of a collision calculated?

The force of a collision is calculated by multiplying the mass of an object by its acceleration. This is known as Newton's second law of motion, which states that force equals mass times acceleration.

3. What factors affect the force of a collision?

The force of a collision is affected by the mass, velocity, and direction of the objects involved in the collision. Additionally, the duration of the collision and the nature of the surfaces in contact can also impact the force.

4. How does the force of a collision impact the objects involved?

The force of a collision can cause changes in the motion and shape of the objects involved. If the force is strong enough, it can also result in damage or deformation of the objects.

5. Can the force of a collision be controlled?

The force of a collision can be controlled to some extent by altering the velocity or direction of the objects involved. However, it is ultimately determined by the laws of physics and the properties of the objects in the collision.

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