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Sagot :
The work required to stretch the spring is 350J.
Hooke's Law
This law can be written by the formula: F=kx, where:
F= elastic force (N)
k= spring constant (N/m)
x= linear displacement (m)
Spring Work
For finding the spring work in J, you should apply the formula [tex]W=\frac{k*(\Delta x)^2}{2}[/tex], where:
W= work (J)
k= spring constant (N/m)
x= difference between the linear displacements (m)
The question gives:
x=5 cm=0.05m requires a force of 1.4N
x=8 cm =0.08m
- Step 1 - First, you should find the spring constant from Hooke's law, for x=5 cm and F=1.4N.
[tex]F=kx\\ 1.4=k*0.05\\ \\ k=\frac{1.4}{0.05} =28\frac{N}{m}[/tex]
- Step 2 - Now you can apply the formula for spring work.
[tex]W=\frac{k*(\Delta x)^2}{2}\\ \\ W=\frac{28*(8-3)^2}{2} \\ \\ W=\frac{28*(5)^2}{2}\\ \\ W=\frac{28*25}{2}\\ \\ W=\frac{700}{2}=350J[/tex]
Read more about the spring work here:
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