Exercise 6.40 Part A As part of your daily workout, you lie on your back and pus

Question

Exercise 6.40 Part A 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 85.0 J when you compress the springs a distance of 0.170 m from their uncompressed length. What magnitude of force must you apply to hold the platform in this position? Submit My Answers Give Up Part B How much additional work must you do to move the platform a distance 0.170 m farther? ? Submit My Answers Give Up Part C What maximum force must you apply to move the platform to the position in Part B? Submit My Answers Give Up

Explanation / Answer

A] For two springs in parallel,

F = (k + k')x

=> U = (1/2)(k + k')x2

this will be the energy stored in the system.

therefore, 85 = (1/2)(k+k')0.172

=> k+k' = 5882.35 N/m

therefore, F = 5882.35(0.17) = 1000 N

this is the required force.

B]

W = (1/2)(5882.35)(0.17+0.17)2 - 85 = 255 J

C] F = 5882.35(0.17+0.17) = 2000 N.

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