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 85.0 J when you compress the springs a distance of 0.250 m 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 0.220 m farther? What maximum force must you apply to move the platform a distance 0.220 m farther?

Answer 1

a) F = 680 N, b) W = 215 .4 J , c) F = 1278.4 N

Step-by-step explanation:

a) Hooke's law is

F = k x

To find the displacement (x) let's use the elastic energy equation

`K_(e)` = ½ k x²

k = 2
`K_(e)` / x²

k = 2 85.0 / 0.250²

k = 2720 N / m

We replace and look for elastic force

F = 2720 0.250

F = 680 N

b) The definition of work is

W = ΔEm

W =
`K_(ef)` -
`K_(eo)`

W = ½ k (
`x_(f)`² - x₀²)

The final distance

`x_(f)` = 0.250 +0.220

`x_(f)` = 0.4750 m

We calculate the work

W = ½ 2720 (0.47² - 0.25²)

W = 215 .4 J

We calculate the strength

F = k
`x_(f)`

F = 2720 0.470

F = 1278.4 N