Calculating Spring Constant and Energy: A Practical Guide

In summary, a 0.20-kg mass attached to a spring is pulled back horizontally across a table, increasing the potential energy of the system from zero to 120 J. Ignoring friction, the kinetic energy of the system after the mass is released and has moved to a point where the potential energy has decreased to 80 J can be found using the equations PE=1/2 k*x^2 and KE=1/2 m*v^2. All the forces in the system are conservative, meaning that the fundamental quantity of energy is conserved. It is not necessary to know the distance of the spring to calculate the spring constant or potential energy, as long as the potential energy values at different points are known.
  • #1
laxboi33
9
0
A .20- kg mass attached to a spring is pulled back horizontally across a table so that the potential energy of the system is increased from zero to 120 J. Ignoring friction, what is the kinetic energy of the system after the mass is released and has moved to a point where the potential energy has decreased to 80 J.



PE= 1/2 k*x^2
KE= 1/2 m*v^2
F= -kx


How would I find the spring constant or PE without the distance of the spring?
 
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  • #2
What is the change in potential energy converted into?
 
  • #3
Consider the following:
All the forces in the system are conservative.

What fundamental quantity is conserved?
 
  • #4
laxboi33 said:
How would I find the spring constant or PE without the distance of the spring?

You are told what the potential energy is at each point, so you don't need to know how it was calculated. Just write down the total energy at each point in the most general terms possible, and go from there.
 

FAQ: Calculating Spring Constant and Energy: A Practical Guide

What is the spring constant?

The spring constant, also known as the force constant, is a measure of the stiffness of a spring. It represents the amount of force required to stretch or compress a spring by a certain distance.

How is the spring constant calculated?

The spring constant can be calculated by dividing the force applied to the spring by the resulting change in length or displacement. It can also be found by dividing the force constant by the length of the spring.

What is Hooke's law and how does it relate to calculating spring constant?

Hooke's law states that the force required to stretch or compress a spring is directly proportional to the displacement of the spring. This means that as the spring constant increases, the force required to stretch or compress the spring also increases.

Can the spring constant change?

Yes, the spring constant can change depending on factors such as the material, length, and diameter of the spring. It can also change if the spring has been stretched or compressed beyond its elastic limit, causing permanent deformation.

How is energy related to the spring constant?

The energy stored in a spring is directly proportional to the spring constant. This means that as the spring constant increases, the amount of energy stored in the spring also increases. This relationship is represented by the equation E=1/2kx^2, where E is the energy, k is the spring constant, and x is the displacement of the spring.

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