Calculating Work Done on a Spring with Given Stiffness and Length Changes

In summary, to change the length of a spring from 12 cm to 15 cm, you must do 0.135 Nm of work. This can also be calculated by taking the integral of Kx, where K is the stiffness, and taking the difference between the two given lengths.
  • #1
karobins
7
0

Homework Statement



A spring has a relaxed length of 7 cm and a stiffness of 150 N/m. How much work must you do to change its length from 12 cm to 15 cm?

Homework Equations



F=-kx, W=F(delta)x

The Attempt at a Solution



?? ((.12 m)-(.07 m) * (150 N/m)) = 7.5 N

((.15 m)-(.07 m) * (150 N/m)) = 12 N

(12-7.5 N) * (.15-.12 m) = .135 Nm
 
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  • #2
Welcome to PF.

You need to consider that W = ΔPE

What is the formula for the PE of a spring?
 
  • #3
thanks much for the help!
 
  • #4
i assume you got the answer but if not
a quick way to solve this problem is to
set up a integral.
integrate Kx where K is the stiffness
so it gives you 75x^2
act like relaxed length is initial (or 0) then find difference
from initial your two asking points are (make sure your in m not cm)
ex. rest is 7cm find work 13cm stretched to 15 cm
first limit would be (.13-.07)=.06 next (.15-.07)=.08
just plug these into 75x^2
do F(b)-F(a) and that gives you the answer
 

What is work done on a spring?

Work done on a spring refers to the amount of energy transferred to or from a spring due to a force acting on it. It is calculated by multiplying the force applied to the spring by the distance the spring is displaced.

What factors affect the work done on a spring?

The work done on a spring is affected by the force applied to the spring, the distance the spring is displaced, and the spring constant, which is a measure of the stiffness of the spring.

How is work done on a spring related to potential energy?

The work done on a spring is directly related to the potential energy stored in the spring. As work is done on the spring, potential energy is stored in the form of elastic potential energy. The more work done, the more potential energy is stored in the spring.

Can work be done on a spring without changing its length?

Yes, work can be done on a spring without changing its length if the force applied is perpendicular to the direction of motion. In this case, the work done is equal to zero since the displacement of the spring is also zero.

How is the work done on a spring calculated?

The work done on a spring can be calculated using the formula W = 1/2kx^2, where W is the work done, k is the spring constant, and x is the distance the spring is displaced. Alternatively, it can be calculated by finding the area under the force-displacement curve on a graph.

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