Question

the explorer visited the three places and raised her hand when she reached each of them, where would the change in gravitational potential energy of her hand be greater? The summit of Chimborazo, in Ecuador, which is at a distance of 6,384 km6,384 km from the Earth’s center. The bottom of the Mariana Trench, in the western Pacific ocean, which is nearly 6,370 km6,370 km from the center of the Earth. On the surface of Earth on the Equator line.

Answer 1

The bottom of the Mariana Trench, in the western Pacific ocean, which is nearly 6,370 km

Step-by-step explanation:

The bottom of the Mariana Trench is the deepest point ever found in our planet, and it is the closest to the earth´s center, rememeber that gravitational potential energy decreases as height increases, so the place where the change of gravitational potential energy would be the greatest, not meaning that that would be meaningful or feelable, would be the bottom of the Mariana Trench due to its closeness to the center of the Earth.

Answer 2

the Mariana trench

Step-by-step explanation:

To perform this calculation we must use the law of universal gravitation

F = G m M / r²

Where the gravitational potential energy is immediately deducted

U = ∫ F dr

U = - G m M (1 / r - 1 / Ro)

In general the point of Ro is taken at infinity so that here the energy is zero

Therefore, for this problem we will use the equation

U = - G m M / r

Let's calculate the distance, for the three requested points

-Ecuador

R = 6370 km (1000 m / 1 km)

R = 6.370 10 6 m

- Mariana Trench

This is 11 km deep

R = 6370 -11 km = 6359 km

R = 6.359 106 m

- The Chimborazo

R = 6384 Km

R = 6.384 10 6 m

We can appreciate that if we introduce these values ​​in the formula, the one that gives the greatest change would be the one with the least distance. Let's calculate it,

- Ecuator

U = - (G mM) / (6.370 106)

U = - (GmM) 1.5699 10-7 J

- mariana trench

U = - (GmM) 1 / 6,359 106

U = - (GmM) 1.5725 10-7 J

- Chimborazo

U = - (GmM) 1 / 6,384 106

U = - (GmM) 1.5664 10 -7 J

Here we can see that the greatest value is that of the Mariana trench