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## Homework Statement

Alright, this one's been bothering me.

An engineer is designing a spring to be placed at the bottom of an elevator shaft. If the elevator cable should break when the elevator is at a height

*h*above the top of the spring, calculate the value that the spring stiffness constant

*k*should have so that passengers undergo an acceleration of no more than 5.0

*g*when brought to rest. Let

*M*be the total mass of the elevator and passengers.

## Homework Equations

W=[itex]\frac{1}{2}[/itex]kd[itex]^{2}[/itex]

W=Fd

E[itex]_{p}[/itex]=Mgh

## The Attempt at a Solution

I'm assuming that the potential energy will be equal to the kinetic energy, so:

W=Mgh=Fd

Mgh=Mad

plugging in 5.0g for

*a*I get h=5.0d, d=[itex]\frac{h}{5.0}[/itex]

Mgh=[itex]\frac{1}{2}[/itex]k([itex]\frac{h}{5.0}[/itex])[itex]^{2}[/itex]

=[itex]\frac{1}{2}[/itex]k([itex]\frac{h^{2}}{25}[/itex])

=[itex]\frac{kh^{2}}{50}[/itex]

50Mgh=kh[itex]^{2}[/itex]

k=[itex]\frac{50Mg}{h}[/itex]

However, the answer in my textbook is [itex]\frac{12Mg}{h}[/itex]. Any help here? I have a strange feeling that I did the first part wrong making the E[itex]_{p}[/itex] equal to E[itex]_{k}[/itex].