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## Homework Statement

The above image shows Yelena Isinbayeva (64.1 kg) at a point in her vault where the pole is maximally deflected (Δx = 1.63 m). The pole has a bending stiffness of 1091 N/m and behaves according to Hooke's Law. At this point in the vault, her vertical velocity is 3.25 m/s and she is 2.48 m above the ground.

How much work was done be gravity during the time the vaulter went from 2.48 m above the ground to her peak height?

## Homework Equations

P=W/t

work done = change in energy

Hooke's Law: F

_{s}=kΔx

W

_{s}=(1/2)kΔx

^{2}

KE=(1/2)mv

^{2}

PE

_{g}=mgh

SE=(1/2)kΔx

^{2}

Total energy = KE+PE+SE

W=FΔd

I have already calculated the following from previous questions

Work done on the pole = 1449.34J

SE stored in the pole = 1449.34J

Force applied to the pole = 1778.33N

KE in vertical direction = 338.53J

PE

_{g}= 1559.48J

Peak height of her centre of mass = 5.32m

## The Attempt at a Solution

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I tried:

W=FΔd

W=(1778.33)(5.32-2.48)

W=5050.46

PE

_{g}=mgh

PE

_{g}=(64.1)(9.81)(5.32-2.48)

PE

_{g}=1785.85

W

_{s}=(1/2)(1090)(5.32)(2.48)

^{2}

W

_{s}=4395.75

These answers are all incorrect. I'm not sure how to approach this problem in another way.

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