Question

The gravitational force between a 4.9 kg backpack and a second backpack of unknown mass is
3.74 x 10-10 N. The distance between the centers of the backpacks is 2.5 m.
Calculate the mass of the second backpack.
Write your answer using two significant figures.
kg
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Answer 1

Taking into account the Law of Universal Gravitation, the mass of the second backpack is 7.15 kg.

The Law of Universal Gravitation is one of the laws of physics formulated by Isaac Newton. Describe the gravitational interaction, and establish a relationship of proportionality of the gravitational force with the mass of the bodies.

The Law of Universal Gravitation  states that:

Every material particle attracts any other material particle with a force directly proportional to the product of the masses of both and inversely proportional to the square of the distance that separates them.

Mathematically it is expressed as:

$F=G\frac{m1m2}{r^{2} }$

Where m1 and m2 are the masses of the interacting bodies; r the distance between them and G a universal constant that receives  the name of the gravitation constant, whose value is G = 6.67×10⁻¹¹ $\frac{Nm^{2} }{kg^{2} }$.

In this case, you know:

• F= 3.74×10⁻¹⁰ N

• G= 6.67×10⁻¹¹ $\frac{Nm^{2} }{kg^{2} }$

• m1= 4.9 kg
• m2= ?
• r= 2.5 m

Replacing:

$3.74x10^{-10}N =6.67x10^{-11}\frac{Nm^{2} }{kg^{2} }\frac{4.9 kgxm2}{(2.5 m)^{2} }$

Solving:

$3.74x10^{-10}N =6.67x10^{-11}\frac{Nm^{2} }{kg^{2} }x0.784\frac{kg}{m^{2} }xm2$

$\frac{3.74x10^{-10}N}{6.67x10^{-11}\frac{Nm^{2} }{kg^{2} }x0.784\frac{kg}{m^{2} } } =m2$

7.15 kg= m2

Finally, the mass of the second backpack is 7.15 kg.

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