As part of your daily workout, you lie on your back and push with your feet agai

Question

As part of your daily workout, you lie on your back and push with your feet against a platform attached to two stiff springs arranged side by side so that they are parallel to each other. When you push the platform, you compress the springs. You do an amount of work of 78.0 J when you compress the springs a distance of 0.210 m from their uncompressed length.

Part A

What magnitude of force must you apply to hold the platform in this position?

Part B

How much additional work must you do to move the platform a distance 0.210 m farther?

Part C

What maximum force must you apply to move the platform to the position in Part B?

I have no idea how to solve this problem. Thanks!

Explanation / Answer

W =78 J ,x =0.21 m

Work done by spring force equal toc hange in potential energy in spring

W = (1/2)kx^2

k = 2W/x^2

k = (2*78)/(0.21*0.21)

Spring costant k =3537.4 N/m

Part A:

From Hooks law

F =kx

F = 3537.4*0.21= 742.85 N

Part B: W1 = 78 J

W2 = (1/2)k(2x)^2 = 0.5*3537.4*(2*0.21)^2

W2 =312 J

Additional work = W2 -W1 =312 -78 =234 J

Part C:

F =k*2x = 3537.4*2*0.21

F =1485.7 N

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