Classical Mechanics

Newton's Law of Gravity

Gravitational Potential Energy

         

What is the approximate gravitational potential energy of the two-particle system, of masses 5.4 kg5.4\text{ kg} and 2.9 kg,2.9 \text{ kg}, separated by a distance of 15.0 m?15.0\text{ m}?

Assumptions and details

  • The universal gravitational constant is G=6.67×1011 Nm2/kg2.G=6.67 \times 10^{-11} \text{ N}\cdot\text{m}^2\text{/kg}^2.

Consider an xyxy-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 m.3.6\text{ m}. The masses of particles A and B are 24 kg24\text{ kg} and 12 kg,12\text{ kg}, respectively. If particle B is released from rest, what is the kinetic energy of B when it has moved 0.1 m0.1\text{ m} toward A?

Assumptions and Details

  • The universal gravitational constant is G=6.67×1011 Nm2/kg2.G=6.67 \times 10^{-11} \text{ N}\cdot\text{m}^2\text{/kg}^2.

The mean diameter of Mars is 6.7×103 km6.7\times 10^3\text{ km} and its mass is 6.7×1023 kg.6.7\times 10^{23}\text{ kg}. What is the approximate escape speed on Mars?

Assumptions and Details

  • The universal gravitational constant is G=6.67×1011 Nm2/kg2.G=6.67 \times 10^{-11} \text{ N}\cdot\text{m}^2\text{/kg}^2.

Four identical particles are forming a square with side length 12.0 m,12.0\text{ m}, as shown in the above figure. Then the side length of the square is reduced to 4.0 m.4.0\text{ m}. If the mass of each particles is 19.0 kg,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=6.67×1011 Nm2/kg2?G=6.67 \times 10^{-11} \text{ N}\cdot\text{m}^2\text{/kg}^2 ?

If a 6000 kg6000 \text{ kg} space rocket is launched vertically from the surface of the Earth with initial energy 7.0×1011 J,7.0 \times 10^{11} \text{ J}, what will be the kinetic energy of the space rocket when it is 1.4×107 m1.4 \times 10^7 \text{ m} from the center of the Earth, assuming that the mass and the radius of the Earth are 6.0×1024 kg6.0 \times 10^{24}\text{ kg} and 6.4×106 m,6.4 \times 10^6 \text{ m}, respectively?

Assumptions and Details

The universal gravitational constant is G=6.67×1011 Nm2/kg2.G=6.67 \times 10^{-11} \text{ N}\cdot\text{m}^2\text{/kg}^2.

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