Answered: gravitation with the Earth as m2 and…

Glencoe Physics: Principles and Problems, Student Edition

1st Edition

ISBN:9780078807213

Author:Paul W. Zitzewitz

Publisher:Paul W. Zitzewitz

Chapter7: Gravitation

Section: Chapter Questions

Problem 5STP

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So let's consider a person with a mass of 51.0 kg standing on the Earth. To find the gravitational force on the person, we'll again use Newton's law of universal gravitation with the Earth as

m₂

and the radius of the Earth for the distance

F =

GmM_E

R_E²

Now all we need to do is substitute values and calculate. We already said

m = 51.0 kg,

and we know

G = 6.67 ✕ 10⁻¹¹ N · m²/kg².

The Earth is not a perfect sphere, but, its average radius is

R_E = 6.37 ✕ 10⁶ m.

The mass of the Earth is

M_E = 5.97 ✕ 10⁻²⁴ kg.

We can then substitute these values in the following formula. (Enter your answer in N.)

F =

(6.67 ✕ 10⁻¹¹ N · m²/kg²)(51.0 kg)(5.97 ✕ 10²⁴ kg)

(6.37 ✕ 10⁶ m)²

(A) = _______ N

Now let's compare this result to the person's weight (in N) found by multiplying the person's mass by g (or, that is,

w = mg)

where

g = 9.80 m/s².

w = (51.0 kg)(9.80 m/s²) =(b) __________________ N

You should have found that these two methods give about the same result! This tells us that g, the acceleration due to gravity, is actually determined by mass and radius of the Earth—or the Moon, or Mars, or whatever planet we happen to be standing on.

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