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 76.0 J when you compress the springs a distance of 0.170 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?

Answer 1

`894.12\ \text{N}`

`284.013\ \text{J}`

Step-by-step explanation:

U = Energy = 76 J

x = Displacement of spring = 0.17 m

k = Spring constant

Energy is given by

`U=(1)/(2)kx^2\\\Rightarrow k=(2U)/(x^2)\\\Rightarrow k=(2* 76)/(0.17^2)\\\Rightarrow k=5259.51\ \text{Nm}`

Force is given by

`F=kx\\\Rightarrow F=5259.51* 0.17\\\Rightarrow F=894.12\ \text{N}`

The magnitude of force must you apply to hold the platform is
`894.12\ \text{N}`.

Now
`x=0.17+0.2=0.37\ \text{m}`

`U=(1)/(2)kx^2\\\Rightarrow U=(1)/(2)* 5259.51* 0.37^2\\\Rightarrow U=360.013\ \text{J}`

Additional energy

`360.013-76=284.013\ \text{J}`