Why is the energy stored in a spring proportional to 1/2 * distance * force?

  • Context: High School 
  • Thread starter Thread starter GeneralOJB
  • Start date Start date
  • Tags Tags
    Energy Spring
Click For Summary
SUMMARY

The energy stored in a spring is calculated using the formula 1/2 * distance * maximum-force due to the non-constant nature of the force applied during compression. Unlike a constant force scenario, where work is simply force multiplied by distance, the force exerted by a spring increases linearly as it is compressed. To derive this relationship accurately, calculus is employed to integrate the instantaneous force over the incremental distance of compression. This method confirms that the energy stored in a spring is indeed half of the product of the distance compressed and the maximum force exerted.

PREREQUISITES
  • Understanding of Hooke's Law and spring mechanics
  • Basic knowledge of calculus, specifically integration
  • Familiarity with the concept of work in physics
  • Knowledge of linear force applications
NEXT STEPS
  • Study the derivation of Hooke's Law and its applications in real-world scenarios
  • Learn about the principles of work and energy in physics
  • Explore calculus techniques for integrating variable forces
  • Investigate the behavior of different types of springs under various loads
USEFUL FOR

Physics students, mechanical engineers, and anyone interested in understanding the principles of energy storage in elastic materials.

GeneralOJB
Messages
42
Reaction score
0
Why is the energy stored in a spring 1/2 * distance * force? Isn't work just force * distance?
 
Physics news on Phys.org
GeneralOJB said:
Why is the energy stored in a spring 1/2 * distance * force? Isn't work just force * distance?

The full force is not applied for the full distance.

In the simple case of a constant force over a fixed distance you can just multiply force by distance. But in the case of a spring being compressed, the force is not constant.

You could approximate the answer by analyzing the situation in small steps... You compress the spring the first 1/10th of the distance using 1/10th of the full force, the next 1/10th of the instance using 2/10th of the total force and so on. This approach would give you an answer that is pretty close.

An exact answer can be obtained by using calculus and integrating instantaneous force over incremental distance. That answer turns out to be 1/2 * distance * maximum-force
 
Last edited:
Thanks, I understand now.
 

Similar threads

High School Curious about Work and Energy Consumption
  • · Replies 8 ·
Replies
8
Views
2K
High School Why is my experimental spring constant an order of magnitude off?
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Work-Energy Theorem for Moving Block and Spring System?
  • · Replies 4 ·
Replies
4
Views
3K
High School How will a spring stretch in the following cases?
  • · Replies 17 ·
Replies
17
Views
2K
Undergrad Modeling a (rotating) mass impact on a preloaded (rotational) spring
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Questions about a spring and its principle
  • · Replies 9 ·
Replies
9
Views
3K
Undergrad Solving the Block-on-Spring Problem Using Forces
  • · Replies 11 ·
Replies
11
Views
5K
Undergrad How come you have to use work energy to find v0 of spring?
  • · Replies 9 ·
Replies
9
Views
2K
Undergrad Looking to find the amount of energy stored in a clock spring
  • · Replies 2 ·
Replies
2
Views
3K
High School Why Does a Spring Return to Its Original Position After Being Stretched?
  • · Replies 9 ·
Replies
9
Views
3K