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

AI Thread Summary
To determine the force needed to hold the leg press platform, the work done in compressing the springs is used to find the spring constant (k) with the formula (1/2)k(0.27^2) = 72 J. Once k is calculated, the force can be found using F = kx for the initial compression of 0.27 m. For the additional work required to compress the platform another 0.27 m, the work done is calculated using (1/2)k((0.54^2)-(0.27^2)). The maximum force for the additional compression can also be determined with F = kx for the new distance. This approach effectively solves the problem of force and work in the context of spring compression.
rrastam
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Here's the question that is giving me problems
PLEASE HELP!

Leg Presses. 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 72.0 J of work when you compress the springs 0.270 m from their uncompressed length.

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

(b) How much additional work must you do to move the platform 0.270 m farther, and what maximum force must you apply?
 
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Spring law: force= spring constant * distance compressed. (F= kx)

energy: integrating kx dx from a to b, the work done in compressing from a to b is
(1/2)k x2 evaluated between a and b: (1/2)k(b2-a2)

You compress the springs from 0 to .27 and do 72 J of work so
(1/2)k(.272)= 72. You can solve that for k.

Once you know k, You can answer (a) with F= kx.

Moving the platfork "0.270 m farther", you move it from 0.270 to 0.540 m. Since you now know k, you can answer the first part of (b) with (1/2)k((.54)2-(.27)2) and the second part with F= kx.
 
Thank you...u really helped me out
 

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