A Spring in a Conservation of Energy Problem?

In summary, the conversation is about finding the maximum compression of a spring, given the mass of a block, the height of a ramp, and the spring constant. The person suggests using conservation of energy and the equation E_e = (1/2)kx^2 to solve the problem. They also mention the possibility of using elastic potential energy and ultimately solve the problem with the help of others.
  • #1
PhysicsPhun
55
0
Not totally lost but for the most part.. I'm pretty lost..

A Block of mass m = 7.20 kg is released from rest at a heigh of H = 9 m on a curved frictionless ramp. At the foot of the ramp is a spring whose spring constant is k = 306 N/m. What is the maximum compression of the spring, x?

Alright so using conservation of energy, i got the final velocity to be 13.2816 m/s. The "ramp" becomes flat, and is frictionless, so there is no acceleration, correct?
This is where i am stuck.
The only thing i can think of to find the maximum compression of the spring is: F = -Kx

Is there anything else i can do? Or is there something i am missing?

Thanks.
 
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  • #2
You'd have an easier time with a simpler energy argument.

[tex]E_e = \frac{1}{2}kx^2[/tex]

Where [itex]E_e[/itex] is the elastic energy due to the compression in the spring.

cookiemonster
 
  • #3
Elastic potential energy?

Would that just be the potential energy before the block begins to move at the top of the ramp?
 
  • #4
Wow, I got it. Thanks alot. Very much appreciated.
 

1. What is a spring in a conservation of energy problem?

A spring in a conservation of energy problem refers to a simple system in which a spring is attached to an object and used to store and release energy. This type of system is often used in physics experiments to demonstrate the principles of energy conservation.

2. How does a spring store and release energy?

A spring stores energy by being compressed or stretched from its natural length. This potential energy is then released when the spring returns to its original length. The amount of energy stored in a spring depends on its stiffness and the amount it is compressed or stretched.

3. What is the relationship between a spring's potential energy and its displacement?

The potential energy of a spring is directly proportional to its displacement from its natural length. This means that the more the spring is compressed or stretched, the more potential energy it will have. This relationship is described by the equation PE = 1/2 kx², where k is the spring constant and x is the displacement.

4. How does a spring in a conservation of energy problem demonstrate the principle of energy conservation?

The principle of energy conservation states that energy cannot be created or destroyed, only transferred from one form to another. In a spring in a conservation of energy problem, the potential energy stored in the spring is converted into kinetic energy as the spring returns to its natural length. This demonstrates the conservation of energy in the system.

5. What are some real-life examples of a spring in a conservation of energy problem?

One common example is a pogo stick, where the energy stored in the compressed spring is used to propel the rider upwards. Another example is a bungee cord, where the energy stored in the stretched cord is used to bounce the person back up after they have jumped off a height. Springs are also used in many mechanical devices such as shock absorbers and trampolines, which utilize the principles of energy conservation.

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