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 83.0 JJ when you compress the springs a distance of 0.160 mm from their uncompressed length. What magnitude of force must you apply to hold the platform in this position? How much additional work must you do to move the platform a distance of 0.220 m farther? What maximum force must you apply to move the platform a distance of 0.220 m farther?

Answer 1

Explanation:

a) If you do a work done of about 83.0 J and if we consider that there is no energy lose then the energy stored in the spring will be 83.0 J. So we can write it as,

U = 83.0 J

Energy stored in spring is,

U = $\frac{1}{2}kx^{2}$

∵ k is the spring constant

∵ x is the distance that tells us how much the spring is compressed or stretched.

We can solve the problem by separately considering the springs or we take these two springs as one spring. So the spring constant ill be

k = $\frac{2U}{x^{2} }$

  = 2(83)/(0.160)²= 6484 N/m

now the force needed to keep the spring compressed

F = kx = $\frac{2U}{x}$ = 1037 N

b) The additional work done can be find out by the change n potential energy due to compression of spring.

Final potential energy = $\frac{1}{2}k 2x^{2} = 4U = 4(83) = 332 J$

The additional work 332-83 = 249 J

c) F = k(2x)

     = (6484)(2)(0.220) = 2851 N