Question

Two men each have a mass of 90 kg. If the gravitational force between them is 8.64 x 10^-8 N, how far apart are they?

Answer 1

Given:

Mass of man 1(m1): 90 Kg

Mass of man 2 (m2):90 Kg

Distance between the two men (r) = x m

F(gravitational force) = 8.64 x 10^-8 N

Now we know that

Newton's law of universal gravitation states that all particle attract every other particle in the universe with a force . This force is directly proportional to the product of their masses. Also this is inversely proportional to the square of the distance between their centers.

This is mathematically represented as

F= (G X m1 x m2) /r∧2

where F is the gravitational force acting between the charged particles measured in N

r is the distance between the two charges measured in m

G is the gravitational constant which has a value of 6.674×10^-11 Nm^2 kg^-2

m1 and m2 are the masses of the objects measured in Kg

Now substituting the given values in the above equation we get

8.64 x 10^-8 = (6.674 X 10∧-11 x 90 x 90)/(r∧2)

Thus r=0.399 m

F= 3.3 X10∧-50 N

Answer 2

Step-by-step explanation:

Given that,

Two men has equal mass

Then, M1 = M2 = M = 90kg

Gravitational force between them is

F = 8.64× 10^-8N.

Distance apart r=?

So we want to find distance apart

Using the gravitational law formula

F = GM1M2 / r²

Where G is gravitational constant

G = 6.67 × 10^-11 Nm²/kg²

Since M1 = M2 = 90kg

Then,

F = GM² / r²

8.64 × 10^-8 = 6.67 × 10^-11 × 90² / r²

Cross multiply

8.64 × 10^-8 × r² = 6.67 × 10^-11 × 90²

r² = 6.67 × 10^-11 × 90² / 8.64 × 10^-8

Then,

r ² = 6.253

r = √6.253

r = 2.5m

The distance between the men is 2.5m