Two trucks with equal mass are attracted to each other with a gravitational force of 5.3 x 10 -4 N. The trucks are separated by a distance of 2.6 m. What is the mass of either of the trucks?

where [tex]G =6.67408*10^{-11} m^3/kgs^2[/tex] is the gravitational constant on Earth. [tex]M = M_1 = M_2[/tex] is the masses of the 2 objects. and R = 2.6m is the distance between them.

[tex]F_G = 5.3*10^{-4}N[/tex] is the attraction force.

[tex]5.3*10^{-4} = 6.67408*10^{-11}\frac{M^2}{2.6^2}[/tex]

[tex]7941265 = \frac{M^2}{2.6^2}[/tex]

[tex]M^2 = 53682948.76[/tex]

[tex]M = \sqrt{53682948.76} \approx 7327 kg[/tex] or 7.3 tons

Lanuel Lanuel · Answer 2 · 2021-12-10T12:54:19+01:00

The mass of either of the trucks is equal to 7,329.06 kilograms.

Given the following data:

Gravitational force = [tex]5.3 \times 10^{-4}\; Newton[/tex]

Radius = 2.6 meters

Scientific data:

Gravitational constant = [tex]6.67\times 10^{-11}[/tex]

To determine the mass of either of the trucks, we would apply Newton's Law of Universal Gravitation:

Note: The mass of the the two trucks are equal.

Mathematically, Newton's Law of Universal Gravitation is given by the formula:

[tex]F = G\frac{M^2}{r^2}[/tex]

Where:

F is the gravitational force.

G is the gravitational constant.

M is the mass of objects.

r is the distance between center of the masses.

Making M the subject of formula, we have:

[tex]M = \sqrt{ \frac{Fr^2}{G}}[/tex]

Substituting the given parameters into the formula, we have;

[tex]M = \sqrt{ \frac{5.3 \times 10^{-4}\;\times \;2.6^2}{6.67\times 10^{-11}}}\\\\M=\sqrt{\frac{5.3 \times 10^{-4}\;\times \;6.76}{6.67\times 10^{-11}}} \\\\M = \sqrt{5.37 \times 10^7}[/tex]

Mass, M = 7,329.06 kg

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