Work to Stretch Spring from 35cm to 40cm

In summary, the conversation discusses finding the work needed to stretch a spring from its natural length of 35 cm to 40 cm, and finding the spring constant through the use of a ratio between known and unknown energies.
  • #1
TG3
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Homework Statement


Suppose 2 J is needed to stretch a spring from it's natural length of 35 cm to 42 cm. How much work is needed to stretch it from 35 cm to 40 cm?

Homework Equations


W=FD
F = KX

The Attempt at a Solution



2 = 12K
K= 1/6

Work = Integral from .35 to .4 of (1/6)X
(1/6)(x^2/2) from .35 to .4.
.013 - .010 = .033
Wrong.
 
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  • #2
W=1/2 kx^2

so from 35 cm to 42 cm, the extension is 7 cm. The work done in this extension is 2J

find k.

Now when you get the value for k, find the extension from 35cm to 40cm and put it back into the formula W=1/2kx2
 
  • #3
Recognising that W is proportional to x^2 you could write the ratio of the known and unknown energies equal to the square of the ratio of the two extensions. The unknown spring constant vanishes in the division so you don't have to worry about calculating it.

2/W = (0.07)^2 / (0.05)^2
 

Related to Work to Stretch Spring from 35cm to 40cm

1. How does the force applied to a spring affect its length?

The force applied to a spring is directly proportional to its change in length, according to Hooke's Law. This means that the greater the force applied, the greater the change in length of the spring.

2. How can the length of a spring be increased?

The length of a spring can be increased by applying a force to stretch it. This can be done by pulling or pushing on the ends of the spring, or by hanging weights from it. The amount of force needed to stretch the spring depends on its stiffness or spring constant.

3. What is the relationship between the length and stiffness of a spring?

The stiffness of a spring, measured by its spring constant, is inversely proportional to its length. This means that a shorter spring will have a higher stiffness and require more force to stretch it compared to a longer spring.

4. Can a spring be stretched indefinitely?

No, a spring has a maximum elastic limit beyond which it cannot be stretched without permanently deforming or breaking. This limit is determined by the material and design of the spring.

5. How can the work done to stretch a spring be calculated?

The work done to stretch a spring can be calculated by multiplying the force applied to the spring by the distance it is stretched. This can be expressed as W = Fd, where W is the work done, F is the force applied, and d is the distance the spring is stretched.

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