Solve Stiffness Question: Work to Change Spring Length

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In summary, the stiffness of a spring directly affects the amount of work required to change its length. The formula for calculating the work done to change the length of a spring is W = 0.5 * k * (Δx)^2, where W is the work done, k is the spring constant, and Δx is the change in length of the spring. Changing the length of a spring will also change its potential energy, with longer springs having greater potential energy. It is easier to change the length of a spring with a lower stiffness, which can be altered by changing its physical properties such as material, diameter, length, or the number of coils.
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clutch12
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Homework Statement



A spring has a relaxed length of 6 cm and a stiffness of 150 N/m. How much work must you do to change its length from 8 cm to 12 cm?


Homework Equations



1/2Ks,f - 1/2Ks,i

The Attempt at a Solution



1/2 Ks,f^2 - 1/2 Ks,i ^2
1/2 (150)(0.06m)^2 - 1/2(150)(0.02)^2
=0.24 N/m

Am i right or is it supposed to be a negative value?
 
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  • #2
Looks good to me! Definitely positive.
 
  • #3
Alright thanks
 

FAQ: Solve Stiffness Question: Work to Change Spring Length

1. How does the stiffness of a spring affect the amount of work required to change its length?

The stiffness of a spring directly affects the amount of work required to change its length. A stiffer spring will require more work to change its length compared to a less stiff spring. This is because the stiffness of a spring is a measure of its resistance to change in length, and the more resistant a spring is, the more work is needed to overcome that resistance and change its length.

2. What is the formula for calculating the work done to change the length of a spring?

The formula for calculating the work done to change the length of a spring is W = 0.5 * k * (Δx)^2, where W is the work done, k is the spring constant, and Δx is the change in length of the spring. This formula is known as the work-energy theorem and is derived from Hooke's law, which states that the force exerted by a spring is directly proportional to its displacement from its equilibrium position.

3. How does changing the length of a spring affect its potential energy?

Changing the length of a spring will also change its potential energy. As the length of a spring increases, its potential energy also increases. This is because the potential energy of a spring is directly proportional to the square of its length. Therefore, the longer the spring, the greater its potential energy.

4. Is it easier to change the length of a spring with a lower or higher stiffness?

It is easier to change the length of a spring with a lower stiffness. This is because a lower stiffness spring will require less work to change its length compared to a higher stiffness spring. Therefore, it will be easier to compress or stretch a lower stiffness spring compared to a higher stiffness spring.

5. How can the stiffness of a spring be changed?

The stiffness of a spring can be changed by altering its physical properties, such as its material, diameter, or length. Increasing the material's strength or thickness will result in a stiffer spring, while decreasing these properties will result in a less stiff spring. Additionally, the number of coils in a spring can also affect its stiffness; more coils will result in a stiffer spring, while fewer coils will result in a less stiff spring.

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