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 80.0 J of work when you compress the springs 0.200 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 0.200 m farther, and what maximum force must you apply?

Explanation:

Energy stored in spring  = 1/2 k x²

80 = 1/2 x k .2²

k = 4000 N /m

Required force = k x

= 4000 x .2

=800 N

b )

Additional work done

= difference in stored elastic energy

= 1/2 k ( x₂² - x₁² )

= .5 x 4000 ( .4² - .2² )

= 240 J

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b. lifting dumbbell weight at 20-degree angle from the body after a 45-degree angle