Spring Constant and Compression Problem

In summary, the conversation discusses finding the amount by which a spring is compressed in a dart gun with a spring constant of 62.50 N/m, given a potential energy of 0.540 J. One equation is used to attempt to solve the problem, but the numbers are mixed up and the answer is incorrect. The correct equation should be 0.540 = 1/2k*x^2, with x representing the displacement or compression of the spring.
  • #1
bbreezy
7
0

Homework Statement



The potential energy stored in the compressed spring of a dart gun, with a spring constant of 62.50 N/m, is 0.540 J. Find by how much is the spring is compressed.

Homework Equations



I know that F=-k*change in x and also spring= 1/2kx^2

The Attempt at a Solution



Using the two formulas above, i tried 1/2(62.5)(x^2) which is .540? but I am getting the wrong answer.. I also tried x=0 and canceling it. I am not sure what I am doing wrong here.
 
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  • #2
What number did you get using the 2nd equation (don't use the first)? Please show your math. And why would you try x = 0?
 
  • #3
I got 9.1125... i did 1/2(62.5)(.540^2)
 
  • #4
I know X is the "displacement" but I am drawing a blank as to what that number is
 
  • #5
Are you saying you solved (1/2)(62.6)x2=0.540 for x, and got the wrong answer?
 
  • #6
I can tell you that the spring is not compressed 9 meters unless you have one big dart gun hehe. Looks like you have your numbers mixed up. Potential energy of a spring is equal to 1/2k*x^2 so your equation should look like this

.540=1/2k*x^2, x is how much the spring is compressed.
 

FAQ: Spring Constant and Compression Problem

What is a spring constant?

A spring constant, also known as a force constant, is a measure of the stiffness of a spring. It is represented by the symbol k and is defined as the force required to stretch or compress a spring by a unit length.

How is spring constant calculated?

The spring constant can be calculated by dividing the force applied to the spring by the displacement caused by that force. In mathematical terms, k = F/x, where k is the spring constant, F is the applied force, and x is the displacement.

What is the relationship between spring constant and compression?

The relationship between spring constant and compression is described by Hooke's Law, which states that the force exerted by a spring is directly proportional to the distance it is stretched or compressed from its equilibrium position. This means that as the compression of the spring increases, the force applied also increases, and the spring constant remains constant.

How does the material of the spring affect the spring constant?

The material of the spring can affect the spring constant because different materials have different levels of stiffness. For example, a steel spring will have a higher spring constant than a rubber spring due to the differences in their elastic properties.

Why is spring constant important in engineering and science?

Spring constant is important in engineering and science because it helps to predict the behavior of springs under different conditions. It is used to design and analyze various mechanical systems, such as suspension systems in cars, to ensure that they function correctly and safely. Additionally, understanding the spring constant can aid in determining the amount of force needed to compress or stretch a spring to a desired length.

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