You pull on a spring whose spring constant is 22 n/m, and stretch it from its equilibrium length of 0.3 m to a length of 0.7 m. estimate the work done by dividing the stretching process into two stages and using the average force you exert to calculate work done during each stage.

W= 4.4 J

Explanation

Elastic potential energy theory

If we have a spring of constant K to which a force F that produces a Δx deformation is applied, we apply Hooke's law:

F=K*x  Formula (1): The force F applied to the spring is proportional to the deformation x of the spring.

As the force is variable to calculate the work we define an average force

 Formula (2)

Ff: final force

Fi: initial force

The work done on the spring is :

W = Fa*Δx

Fa : average force

Δx :  displacement

  :Formula (3)

:  final deformation

 :initial deformation

Problem development

We calculate Ff and Fi , applying formula (1) :

We calculate average force applying formula (2):

We calculate the work done on the spring  applying formula (3) :         :

W= 11N*(0.7m-0.3m) = 11N*0.4m=4.4 N*m = 4.4 Joule = 4.4 J

Work done in stages

Work is the change of elastic potential energy (ΔEp)

W=ΔEp

ΔEp= Epf-Epi

Epf= final potential energy

Epi=initial potential energy

W=ΔEp=  5.39 J-0.99 J = 4.4J

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