Work to Stretch Spring from 35cm to 40cm

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SUMMARY

The discussion focuses on calculating the work required to stretch a spring from 35 cm to 40 cm, given that 2 J is needed to stretch it from 35 cm to 42 cm. The spring constant (K) is determined to be 1/6 N/cm. By applying the work-energy principle and recognizing that work is proportional to the square of the extension, the relationship between the known and unknown work is established, leading to the conclusion that the work needed to stretch the spring from 35 cm to 40 cm is 0.57 J.

PREREQUISITES
  • Understanding of Hooke's Law (F = KX)
  • Knowledge of work-energy principles (W = FD)
  • Ability to perform definite integrals
  • Familiarity with unit conversions (cm to m)
NEXT STEPS
  • Study the derivation of Hooke's Law and its applications in mechanics.
  • Learn about the work-energy theorem in the context of elastic potential energy.
  • Explore the concept of spring constants and their significance in material science.
  • Investigate the use of integrals in calculating work done on variable force systems.
USEFUL FOR

Students in physics or engineering, educators teaching mechanics, and anyone interested in understanding the principles of elasticity and work calculations in springs.

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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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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
 
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
 

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