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Classical Mechanics

Newton's Law of Gravity

Concept Quizzes

Newton's Laws of Gravity
Gravitational Potential Energy
Newton's Law of Gravity - Problem Solving

Challenge Quizzes

Newton's Law of Gravity: Level 2-4 Challenges

Gravitational Potential Energy

What is the approximate gravitational potential energy of the two-particle system, of masses $5.4\text{ kg}$ and $2.9 \text{ kg},$ separated by a distance of $15.0\text{ m}?$

Assumptions and details

The universal gravitational constant is $G=6.67 \times 10^{-11} \text{ N}\cdot\text{m}^2\text{/kg}^2.$

-4.9 \times 10^{-10} \text{ J}

-4.9 \times 10^{-11} \text{ J}

-7.0 \times 10^{-11} \text{ J}

-7.0 \times 10^{-10} \text{ J}

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by Brilliant Staff

Consider an $xy$ -plane in deep space, where two particles A and B are located. Particle A is fixed at the origin and particle B is apart from particle A with a distance of $3.6\text{ m}.$ The masses of particles A and B are $24\text{ kg}$ and $12\text{ kg},$ respectively. If particle B is released from rest, what is the kinetic energy of B when it has moved $0.1\text{ m}$ toward A?

Assumptions and Details

The universal gravitational constant is $G=6.67 \times 10^{-11} \text{ N}\cdot\text{m}^2\text{/kg}^2.$

1.5 \times 10^{-10}\text{ J}

3.0 \times 10^{-9}\text{ J}

3.0 \times 10^{-10}\text{ J}

1.5 \times 10^{-9}\text{ J}

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by Brilliant Staff

The mean diameter of Mars is $6.7\times 10^3\text{ km}$ and its mass is $6.7\times 10^{23}\text{ kg}.$ What is the approximate escape speed on Mars?

Assumptions and Details

The universal gravitational constant is $G=6.67 \times 10^{-11} \text{ N}\cdot\text{m}^2\text{/kg}^2.$

5.2\text{ km/s}

2.3\text{ km/s}

2.8\text{ km/s}

1.6\text{ km/s}

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by Brilliant Staff

Four identical particles are forming a square with side length $12.0\text{ m},$ as shown in the above figure. Then the side length of the square is reduced to $4.0\text{ m}.$ If the mass of each particles is $19.0\text{ kg},$ approximately how much gravitational potential energy of the four-particle system is reduced, assuming that the four particles are point particles?

Assumptions and Details

The universal gravitational constant is $G=6.67 \times 10^{-11} \text{ N}\cdot\text{m}^2\text{/kg}^2 ?$

-2.2 \times 10^{-6}\text{ J}

-2.2 \times 10^{-8}\text{ J}

-3.3 \times 10^{-5}\text{ J}

-3.3 \times 10^{-7}\text{ J}

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by Brilliant Staff

If a $6000 \text{ kg}$ space rocket is launched vertically from the surface of the Earth with initial energy $7.0 \times 10^{11} \text{ J},$ what will be the kinetic energy of the space rocket when it is $1.4 \times 10^7 \text{ m}$ from the center of the Earth, assuming that the mass and the radius of the Earth are $6.0 \times 10^{24}\text{ kg}$ and $6.4 \times 10^6 \text{ m},$ respectively?

Assumptions and Details

The universal gravitational constant is $G=6.67 \times 10^{-11} \text{ N}\cdot\text{m}^2\text{/kg}^2.$

4.4 \times 10^{11}\text{ J}

5.0 \times 10^{11}\text{ J}

3.5 \times 10^{11}\text{ J}

2.9 \times 10^{11}\text{ J}

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by Brilliant Staff