The Moon has instantaneously stopped its orbital motion and its rotation, and was at rest at distance of 384,000 km from Earth. The mass of the moon is 7.3 × 1022 kg. Assume that the only significant gravitational force is due to the Earth. i. What is the initial acceleration of the Moon at the moment its orbital motion stops? What is the acceleration of the Earth due to the Moon’s gravity? ii. What is the potential energy of the Moon, relative to the point r = ∞? iii. Use conservation of energy to determine the velocity of the moon as it impacts the Earth, when r = rE + rM = 6357 + 1736 = 8093 km.
Simple harmonic motion
Simple harmonic motion is a type of periodic motion in which an object undergoes oscillatory motion. The restoring force exerted by the object exhibiting SHM is proportional to the displacement from the equilibrium position. The force is directed towards the mean position. We see many examples of SHM around us, common ones are the motion of a pendulum, spring and vibration of strings in musical instruments, and so on.
Simple Pendulum
A simple pendulum comprises a heavy mass (called bob) attached to one end of the weightless and flexible string.
Oscillation
In Physics, oscillation means a repetitive motion that happens in a variation with respect to time. There is usually a central value, where the object would be at rest. Additionally, there are two or more positions between which the repetitive motion takes place. In mathematics, oscillations can also be described as vibrations. The most common examples of oscillation that is seen in daily lives include the alternating current (AC) or the motion of a moving pendulum.
The Moon has instantaneously stopped its orbital motion and its rotation, and was at rest at distance of 384,000 km from Earth. The mass of the moon is 7.3 × 1022 kg. Assume that the only significant gravitational force is due to the Earth.
i. What is the initial acceleration of the Moon at the moment its orbital motion stops? What is the acceleration of the Earth due to the Moon’s gravity?
ii. What is the potential energy of the Moon, relative to the point r = ∞?
iii. Use conservation of energy to determine the velocity of the moon as it impacts the Earth, when r = rE + rM = 6357 + 1736 = 8093 km.
Trending now
This is a popular solution!
Step by step
Solved in 4 steps
