Work energy theorem to find the maximum compression

In summary, the problem involves a 6.0 kg box moving at 3.0 m/s on a frictionless surface colliding with a light spring of force constant 75N/cm. Using the work energy theorem, the maximum compression of the spring can be found by equating the box's initial kinetic energy of 27 J to the energy stored in the spring at maximum compression. The equation for energy stored in a spring is Fx, where F is the spring force and x is the extension.
  • #1
negatifzeo
66
0

Homework Statement


A 6.0 kg box moving at 3.0 m/s on a horizontal, frictionless surface runs into a light spring of force constant 75N/cm. Use the work energy theorem to find the maximum compression of the spring.


Homework Equations


Wtotal=K2-K1

k1=1/2mv^2=27 J


The Attempt at a Solution


I mus tbe missing something conceptually here, this doesn't appaear to be a difficult problem but I just don't know how to approach it. I don't know the total work, how do I find it?
 
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  • #2
Can you find the kinetic energy of the box before it hits the spring?
 
  • #3
At the maximum compression the box stops
So all the initial Ke is now spring energy.
What's the equation for energy stored in a spring in terms of spring force and extention?
 

Related to Work energy theorem to find the maximum compression

1. What is the work energy theorem?

The work energy theorem is a fundamental principle in physics that states that the work done on an object is equal to the change in its kinetic energy. In other words, if a force is applied to an object, the work done by that force will result in a change in the object's speed or direction.

2. How does the work energy theorem relate to finding maximum compression?

The work energy theorem can be used to calculate the maximum compression of a spring or other object. By equating the work done on the object to the change in its kinetic energy, one can solve for the maximum compression distance that will result in a given change in the object's speed or direction.

3. Can the work energy theorem be applied to all situations?

While the work energy theorem is a powerful tool for understanding the behavior of objects in motion, it is important to note that it is only applicable to situations where the force acting on an object is constant and in the same direction as the object's motion.

4. How does the mass of an object affect the maximum compression distance?

The mass of an object does not directly affect the maximum compression distance, as the work energy theorem is based on the work done by a force, not the mass of the object. However, the mass of an object can indirectly impact the maximum compression distance by affecting the object's kinetic energy, which is related to its mass and velocity.

5. Can the work energy theorem be used to find the maximum compression of a non-spring object?

Yes, the work energy theorem can be applied to any object that experiences a constant force and undergoes a change in speed or direction. This includes non-spring objects such as a ball rolling down a hill or a car being pushed by a constant force. However, it may be more difficult to calculate the work done and change in kinetic energy for non-spring objects compared to a spring, which has a known force-distance relationship.

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