Question

Gravity is a force that every mass exerts on every other mass. When you jump up in the air, not only does the Earth exert a gravitational force on you, but you also exert a gravitational force on the Earth. You, of course, fall back down to the Earth. Which of the following explains why the Earth is not moving toward you when you jump up in the air?
A. Earth exerts a gravitational force on itself.
B. You don't weigh enough to affect Earth's surface.
C. Your mass is very small compared to Earth's mass.
D. Earth's fixed orbit around the Sun keeps it from moving.

Answer 1

Answer:

C. Your mass is very small compared to Earth's mass.

Explanation:

Newton's third law of motion states that:

"When an object A exerts a force (action force) on an object B, object B exerts an equal and opposite force (reaction force) on object A".

If we apply this law to the situation described in the problem, we see that:

- The action force is the gravitational force exerted by the Earth on you

- The reaction force is the gravitational force exerted by you on the Earth

And according to the 3rd law, the magnitude of the two forces is equal:

$F_1 = F_2$ (1)

We also know that, according to Newton's second law of motion, the force on an object is equal to the product between its mass (m) and its acceleration (a):

$F=ma$

So we can rewrite (1) as

$ma = MA$

where

m is the your mass

a is your acceleration

M is the Earth's mass

A is the Earth's acceleration

For the term on the left, we see that m is small, so a is larger (therefore, your acceleration is visible). However, for the term on the right, we see that the mass of the Earth is very large (M is very large), therefore, A is very small, which means that the acceleration of the Earth is almost negligible because the Earth's mass is very large.