Springs, kinetic energy and work

In summary, the 2 kg block attached to a horizontal ideal spring with a spring constant of 200 N/m is given a speed of 5 m/s. Using the conservation of energy equation, the maximum elongation of the spring is calculated to be 0.5 m.
  • #1
eprparadox
138
2

Homework Statement


A 2 kg block is attached to a horizontal ideal spring with a spring constant of 200 N/m. When the spring has its equilibrium length the block is given a speed of 5 m/s. What is the maximum elongation of the spring?

A. 0
B. 0.05 m
C. 5 m
D. 10 m
E. 100 m


Homework Equations


Conservation of Energy: E(initial) = E(final)
1/2*m*vi^2 + 1/2*k*xi^2 = 1/2*m*vf^2 + 1/2*k*xf^2


The Attempt at a Solution


At the point where it has a speed of 5 m/s there is only kinetic energy and at max elongation there is only potential energy. So I set 1/2*2*5^2 = 1/2*200*x^2 and I solved for x and I got 0.5 m.

This isn't one of the choices so I'm not sure if I'm doing this incorrectly or if there is an error in the problem.

Thanks ahead of time for any help.
 
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  • #2
eprparadox said:
At the point where it has a speed of 5 m/s there is only kinetic energy and at max elongation there is only potential energy. So I set 1/2*2*5^2 = 1/2*200*x^2 and I solved for x and I got 0.5 m.
Your solution is correct.
 

FAQ: Springs, kinetic energy and work

What is a spring and how does it work?

A spring is a mechanical device that is designed to store and release energy. It works by deforming and storing potential energy when force is applied to it, and then releasing that energy as kinetic energy when the force is removed.

How is kinetic energy related to springs?

Kinetic energy is the energy an object possesses due to its motion. In the case of a spring, the kinetic energy is related to the motion of the spring as it compresses and expands. As the spring is compressed, it gains potential energy, and when it expands, that energy is converted into kinetic energy.

What is the formula for calculating the potential energy stored in a spring?

The formula for calculating the potential energy stored in a spring is PE = 1/2kx², where k is the spring constant (a measure of the stiffness of the spring) and x is the displacement of the spring from its equilibrium position.

How does force affect the work done on a spring?

The work done on a spring is directly proportional to the force applied to it. This means that the more force applied to the spring, the more work it will do in compressing or expanding. The direction of the force also affects the work done, as the work done by the spring is equal to the force applied multiplied by the distance over which the force is applied.

Can the potential energy stored in a spring be converted into other forms of energy?

Yes, the potential energy stored in a spring can be converted into other forms of energy. When a spring is released, the potential energy is converted into kinetic energy, and as the spring oscillates, some of that energy is also converted into heat due to friction. This conversion of energy is known as the law of conservation of energy, which states that energy cannot be created or destroyed, only transformed from one form to another.

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