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Q108P

Expert-verifiedFound in: Page 211

Book edition
10th Edition

Author(s)
David Halliday

Pages
1328 pages

ISBN
9781118230718

**In 1981, Daniel Goodwin climbed 443 m up the exterior of the Sears Building in Chicago using suction cups and metal clips.**

**Approximate his mass and then compute how much energy he had to transfer from biomechanical (internal) energy to the gravitational potential energy of the Earth-Goodwin system to lift himself to that height.****How much energy would he have had to transfer if he had, instead, taken the stairs inside the building (to the same height)?**

- to be transferred from internal energy to Gravitational potential energy of the Earth-Goodwin system is $2.8\times {10}^{5}\mathrm{J}$ .
- Energy to be transferred if stairs are taken is $2.8\times {10}^{5}\mathrm{J}$ .

Height climbed, h = 443 m

**Gravitational potential energy of a system depends on the position of the object from the earth’s surface.**

Formula:

The change in potential energy is define by using following formula.

$\u2206U=mgh$Here, m is the mass, g is the acceleration due to gravity having a value 9.8 $\mathrm{m}/{\mathrm{s}}^{2}$, and h is the height.

Let the mass of man is,

m = 65 kg

He needs to transfer an amount of energy from his internal energy to Gravitational potential energy of the Earth-Goodwin system. This transferred energy is equal to the increase in his gravitational potential energy $\u2206U$.

$\u2206U=mgh\phantom{\rule{0ex}{0ex}}=65\mathrm{kg}\times \left(9.8\mathrm{m}/{\mathrm{s}}^{2}\right)\times 443\mathrm{m}\phantom{\rule{0ex}{0ex}}=2.8\times {10}^{5}\mathrm{J}$

** I**f stairs are taken inside the building but at the same height, he still must overcome the increase in his gravitational potential energy. So, this will be the same as $2.8\times {10}^{5}\mathrm{J}$ .

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