How do I find the maximum compression of a spring?

[lustish]

Homework Statement

A linear elastic spring can be compressed 0.10m by an applied force of magnitude 5.0N. A 4.5kg crate, moving at 2.0m/s, collides with this spring. What will be the maximum compression of the spring?

x= 0.10kg
F= 5.0N
m= 4.5kg
v= 2.0m/s

Homework Equations

I'm not really sure, but I think that this is a law of conservation of energy problem...
E = E'
Eg+Ek+Ee=(Eg+Ek+Ee)'

Ek=0.5(mv)^2

The Attempt at a Solution

I'm just really lost. Any help would be greatly appreciated!

 

[kisengue]

This is indeed a problem of conservation of energy.

As the crate collides with the spring, at some point all the kinetic energy of the crate will have been transferred to the spring. The mathematical expression for energy stored in a spring is E=ky^2/2 where k is the "spring constant" (don't know this in english), and y is the displacement/compression of the spring.

You can find the spring constant from the first part of the problem, where you are told how much the spring compresses when compressed by a given amount of force. When you have k and have calculated the kinetic energy of the crate, you can solve for y.

Good luck!

 

[thomate1]

I can provide some guidance on how to approach this problem. First, it is important to understand the concept of potential energy and how it relates to the compression of a spring. When a force is applied to a spring, it stores potential energy in the form of elastic potential energy. This potential energy can be calculated using the equation Ee = 0.5kx^2, where k is the spring constant and x is the distance the spring is compressed.

In this problem, we are given the force applied to the spring (5.0N) and the distance it is compressed (0.10m). We can use this information to calculate the spring constant, k, using the equation F = kx. Once we have the spring constant, we can use the equation for elastic potential energy to determine the maximum compression of the spring.

Next, we need to consider the collision between the crate and the spring. This is a conservation of energy problem, as you mentioned, and we can use the equation Ei = Ef. The initial energy (Ei) is the kinetic energy of the crate before the collision, which can be calculated using the equation Ek = 0.5mv^2. The final energy (Ef) is the sum of the potential energy stored in the spring and the kinetic energy of the crate after the collision.

By setting Ei = Ef and solving for x, we can determine the maximum compression of the spring. It is also important to consider the direction of the spring's compression and the direction of the crate's velocity to ensure that the signs are correct in the equations.

In summary, to find the maximum compression of a spring, you will need to use the equations for elastic potential energy, kinetic energy, and conservation of energy. Make sure to carefully consider the given information and the direction of motion to accurately solve the problem.