Question

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

1. 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.
2. How much energy would he have had to transfer if he had, instead, taken the stairs inside the building (to the same height)?

Short answer

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

Step-by-step solution

Given data:

Height climbed, h = 443 m

To understand the concept:

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.

$∆U=mgh$
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.

Compute the amount of energy he had to transfer:

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 $∆U$.

$$\begin{gathered} ∆U=mgh \\ =65\mathrm{kg}\times \left(9.8\mathrm{m}/{\mathrm{s}}^2\right)\times 443\mathrm{m} \\ =2.8\times {10}^5\mathrm{J} \end{gathered}$$

Step 4: How much energy would have had to be transferred if he had, instead, taken the stairs inside the building:

If 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 $2.8\times {10}^5\mathrm{J}$.