# Law of Universal Gravitation

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## Law of Universal Gravitation Answer Key

**Instructions:**
Read each question carefully. Choose the answer that best fits the question. Short answer response questions must be responded to in complete sentences. If the question involves calculations, you must show all your math work.

Given:

[math]G=6.67xx10^−11 N(m/kg)^2[/math] and [math]F_g=(Gm_1m_2)/(r^2)[/math]

1.

Explain the Law of Universal Gravitation between two objects in terms of proportionalities.

- The Law of Universal Gravitation states that the force of attraction between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

2.

Two students are sitting 1.50 m apart. One student has a mass of 70.0 kg and the other has a mass of 52.0 kg. What is the gravitational force between them?

- [math]1.62xx10^-7N[/math]
- [math]8.09xx10^8N[/math]
- [math]1.08xx10^-7N[/math]
- [math]1.09xx10^7N[/math]

3.

The Law of Universal Gravitation states that "all objects are attracted to each other by a gravitational force. The strength of the force depends on the mass of each object and the distance between them." According to this law, is there a stronger gravitational force between you and Earth or an elephant and Earth? Why?

- A stronger gravitational force exists between the elephant and Earth because an elephant is more massive than a person. This creates a stronger gravitational force between the elephant and the Earth than there would be between a person and Earth.

4.

As objects move, the force of gravity changes its direction to stay pointed along the line between their centers.

- True
- False

5.

Calculate the gravitational force between two objects when they are [math]7.50xx10^-1m[/math] apart. Each object has a mass of [math]5.00xx10^1kg[/math].

- [math]F_g=(Gm_1m_2)/(r^2)[/math]

[math]F_g=(((6.67xx10^-11(Nm^2))/(kg^2))(5.0xx10^1kg)(5.0xx10^1kg))/(7.50xx10^-1m)^2=2.96xx10^-7N[/math]

6.

What gravitational force does the Moon produce on Earth if the centers of Earth, with a mass of [math]5.98xx10^24kg[/math], and Moon, with a mass of [math]7.35xx10^22kg[/math], are [math]3.84xx10^8m[/math] apart?

- [math]F_g=(Gm_1m_2)/(r^2)[/math]

[math]F_g=((6.67xx10^-11)(5.98xx10^24kg)(7.35xx10^22kg))/(3.84xx10^8m)^2=1.99xx10^20N[/math]

7.

If the gravitational force between two objects of equal mass is [math]2.30xx10^8N[/math] when the objects are [math]10.0m[/math] apart, what is the mass of each object?

- [math]F_g=(Gm_1m_2)/(r^2)[/math], so [math]m^2=((F_g)(r^2))/G[/math]

[math]m^2=((2.30xx10^8)(10.0m)^2)/(6.67xx10^-11N)=3.45xx10^20kg^2[/math]

[math]m=1.86xx10^10kg[/math]

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