Finding Force Constant of Spring: 0.296 kg & 3.3 J

In summary, the problem involves a 0.296 kg mass attached to a spring with a period of 0.18 s and a total energy of 3.3 J. The goal is to find the force constant of the spring, which is calculated using the equation k = m(T/2pi)^2. The correct solution is achieved by rearranging the equation to solve for k and substituting the correct units for T. It is important to double check units when solving equations.
  • #1
redhot209
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Homework Statement


A 0.296 kg mass is attached to a spring and executes simple harmonic motion with a period of 0.18 s. The total energy of the system is 3.3 J. Find the force constant of the spring. Answer in units of N/m.

Homework Equations


k=m(t/2[tex]\pi[/tex])^2

The Attempt at a Solution


k=296(0.18/2[tex]\pi[/tex])^2
I get 0.0002429276699 but it is wrong. Any ideas what i did wrong?
 
Last edited:
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  • #2
Your equation is wrong. The period should be T = 2pi times the square root of (m/k). I believe that your equation has (k/m) instead of (m/k). Hope that helps.
 
  • #3
Note also: you should learn the trick of carrying through your units and checking them... that would have helped you find this error.
 

FAQ: Finding Force Constant of Spring: 0.296 kg & 3.3 J

1. What is the formula for finding the force constant of a spring?

The formula for finding the force constant of a spring is k = F/x, where k is the force constant, F is the applied force, and x is the displacement of the spring.

2. How do I calculate the force constant of a spring with a mass of 0.296 kg and a potential energy of 3.3 J?

To calculate the force constant, you can use the formula k = (2E)/x^2, where E is the potential energy and x is the displacement of the spring. Plugging in the values, we get k = (2*3.3 J)/x^2. The displacement x can be measured by compressing or stretching the spring and recording the change in length.

3. Can the force constant of a spring change?

Yes, the force constant of a spring can change depending on various factors such as the material of the spring, its length, and how it is used. For example, a spring may become stiffer over time due to repeated use or if it is exposed to extreme temperatures.

4. What is the significance of finding the force constant of a spring?

The force constant of a spring is an important measure of its stiffness and ability to resist deformation when a force is applied. It is used in various equations to calculate the displacement, velocity, and acceleration of an object attached to a spring. Knowing the force constant also allows us to predict the behavior of the spring under different conditions.

5. How can I use the force constant to determine the strength of a spring?

To determine the strength of a spring, you can use the formula F = kx, where F is the force applied, k is the force constant, and x is the displacement of the spring. By plugging in the values for force constant and displacement, you can calculate the force required to compress or stretch the spring to a certain length. This can help determine the strength and suitability of the spring for a particular application.

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