Understanding Gravitational Force: Calculating the Pull on a Human by the Earth

Gravitational force is one of the fundamental forces of nature. It is what binds us to the Earth and makes the planets revolve around the sun. For a human, the calculation of the gravitational force exerted by the Earth is both intriguing and practical.

Introduction to Gravitational Force

Gravitational force is the force that attracts a body toward the center of the Earth, or more generally, toward any object with mass. It is the force that keeps our feet firmly planted on the ground and is crucial for our daily lives.

Calculating Gravitational Force with Fmg

The basic equation for calculating the gravitational force on a 50 kg human due to the Earth is given by Fmg, where:

F Force of gravity m Mass of the object (50 kg in this case) g Acceleration due to gravity

At the Earth's surface, the acceleration due to gravity (g) is approximately 9.81 m/s2. Therefore, the force of gravity on a 50 kg human can be calculated as:

[F m times g 50 , text{kg} times 9.81 , text{m/s}^2 490.5 , text{N}]

This calculation provides a straightforward method to understand the gravitational force acting on a human. It is important to note that this force is equal and opposite to the normal force that the ground exerts on the human, as per Newton's third law of motion.

The Universal Law of Gravity (FGMm/r^2)

For a more precise calculation, one could use the universal law of gravitation, which is expressed by the equation F GMm/r^2. Here, the variables represent:

F Force of gravity G Gravitational constant (6.67430 times; 10-11 m3 kg-1 s-2) M Mass of the Earth (5.972 × 1024 kg) m Mass of the human (50 kg) r Distance from the center of the Earth to the human

Given that the Earth's radius (r) is approximately 6.371 × 106 meters, the calculation can be performed as follows:

[F frac{G times M times m}{r^2} frac{6.67430 times 10^{-11} times 5.972 times 10^{24} times 50}{(6.371 times 10^6)^2} approx 490.5 , text{N}]

This confirms the earlier calculation using F mg. However, using the universal law of gravity provides a better understanding of the forces that govern the universe on a larger scale.

Conclusion: Fmg vs. Newton’s Gravitational Law

While the equation F mg is more than sufficient for everyday calculations and practical purposes, using the universal law of gravitation (F GMm/r^2) offers a deeper insight into the nature of gravitational forces. It is a reminder of the complex and interconnected forces that govern our universe.

Related Keywords

Gravitational force, universal law of gravity, Newton's second law, acceleration due to gravity