Question

As part of your daily workout, you lie on your back and push with your feet against a platform attached to two stiff ideal 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 0.180 m from their uncompressed length.
What magnitude of force must you apply to hold the platform in this position?

Answer 1

Answer:

The magnitude of force must you apply to hold the platform in this position = 888.89 N

Explanation:

Given that :

Workdone (W) = 80.0 J

length x = 0.180 m

The equation  for this  work done by the spring is expressed as:

$W = \frac{1}{2}k_{eq}x^2$

Making the spring constant $k_{eq}$ the subject of the formula; we have:

$k_{eq} = \frac{2W}{x^2}$

Substituting our given values, we have:

$k_{eq} = \frac{2*80}{0.180^2}$

$k_{eq} = 4938.27 \ N.m^{-1}$

The magnitude of the force that must be apply  to the hold platform in this position is given by the formula :

$F = k_{eq}x$

$F = 4938.27*0.180$

F = 888.89 N