A typical adult human has a mass of about 70 kg. (a) What force does a full moon exert on such a human when it is directly overhead with its center 378,000 km away? (b) Compare this force with the force exerted on the human by the earth

Verified step by step guidance

1. Step 1: Begin by understanding the concept of gravitational force, which is given by Newton's law of universal gravitation. The formula is: $F=\frac{GmM}{r^2}$, where $F$ is the gravitational force, $G$ is the gravitational constant, $m$ and $M$ are the masses of the two objects, and $r$ is the distance between the centers of the two objects.
2. Step 2: Calculate the gravitational force exerted by the moon on the human. Use the mass of the moon, which is approximately $7.35\times {10}^{22}$ kg, the mass of the human $70$ kg, and the distance $378000$ km (convert this to meters). Plug these values into the gravitational force formula.
3. Step 3: Calculate the gravitational force exerted by the Earth on the human. Use the mass of the Earth, which is approximately $5.97\times {10}^{24}$ kg, the mass of the human $70$ kg, and the average radius of the Earth $6371$ km (convert this to meters). Use the gravitational force formula again.
4. Step 4: Compare the two forces calculated in steps 2 and 3. This will involve dividing the force exerted by the moon by the force exerted by the Earth to find the ratio of the two forces.
5. Step 5: Reflect on the results. Consider why the force exerted by the moon is much smaller than the force exerted by the Earth, despite the moon's significant mass. This is due to the much larger distance between the moon and the human compared to the distance between the Earth and the human.

Key Concepts

Gravitational Force

Gravitational force is the attractive force between two masses. It is calculated using Newton's law of universal gravitation, which states that the force is proportional to the product of the masses and inversely proportional to the square of the distance between their centers. This concept is essential for determining the force exerted by the moon on a human.

Mass and Distance

Mass and distance are critical factors in calculating gravitational force. The mass of the objects involved, such as the moon and the human, directly affects the magnitude of the force. The distance between the objects' centers, in this case, 378,000 km, is crucial as the force decreases with the square of the distance, highlighting the importance of these parameters in gravitational calculations.

Comparison of Forces

Comparing forces involves analyzing the relative magnitudes of different forces acting on an object. In this scenario, it requires calculating the gravitational force exerted by both the moon and the Earth on the human and comparing them. This concept helps understand the dominance of Earth's gravitational pull due to its larger mass and closer proximity compared to the moon.