Calculating Work Done by a Spring: A Simple Solution

In summary, the conversation discusses a problem involving finding the work done in stretching a spring with a force constant of 2.5 x 10^3 N/m by certain distances. The correct answer to part (a) is 4.5 J and to part (b) is 3.5 J. The correct formula is W=1/2kx^2. Additionally, the conversation briefly mentions the standard SI unit for length, which is answered as meters (m).
  • #1
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[SOLVED] Easy Spring Constant Question

A particular spring has a force constant of 2.5 x 10^3 N/m. (a) How much work is done in stretching the relaxed spring by 6.0 cm? (b) How much more work is done in stretching the spring an additional 2.0 cm?



I am using W=1/2kx^2 but I am not completely sure.



Well the answer are a. 4.5 J and b. 3.5 J. When I plug in I get W=1/2(2500)(8)^2. I am getting the answers 45000 and 35000. I think I am using the right equation I am just multiplying wrong or something..
 
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  • #2
What is the standard SI unit for length?
 
  • #3
Ah man! I can't believe I missed that. Thank you!
 

1. What is a spring constant?

A spring constant, also known as the force constant or stiffness, is a measure of how much force is needed to stretch or compress a spring by a certain distance.

2. How do you calculate the spring constant?

The spring constant is calculated by dividing the force applied to the spring by the resulting change in length or displacement of the spring. This can be represented by the equation F = kx, where F is the force applied, k is the spring constant, and x is the displacement.

3. What are the units of spring constant?

The units of spring constant depend on the system of units being used. In the SI system, the unit of spring constant is Newtons per meter (N/m). In the Imperial system, the unit is pounds-force per inch (lbf/in).

4. How does the spring constant affect the behavior of a spring?

The spring constant determines the stiffness of the spring. A higher spring constant means a stiffer spring, which requires more force to stretch or compress. A lower spring constant means a more flexible spring, which requires less force to stretch or compress. The spring constant also affects the frequency of oscillation of a spring mass system.

5. Can the spring constant change?

Yes, the spring constant can change depending on the material, length, and diameter of the spring. The temperature and environment can also affect the spring constant. In some cases, a spring can experience fatigue or wear and tear, causing the spring constant to decrease over time.

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