The weight of a child at a height of 3.6 × 10^6 m from the Earth's surface

To calculate the weight of the child at a height of 3.6 × 10^6 m from the Earth's surface, we need to understand the concept of gravitational force and how it changes with distance.

Gravitational Force
Gravitational force is the force of attraction between two objects due to their masses. It is responsible for keeping objects on the Earth's surface and governs the motion of planets and other celestial bodies.

Newton's Law of Universal Gravitation
Newton's Law of Universal Gravitation states that the force of attraction between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. Mathematically, it can be represented as:

F = G * (m1 * m2) / r^2

Where:
F is the gravitational force
G is the gravitational constant (approximately 6.67430 × 10^-11 Nm^2/kg^2)
m1 and m2 are the masses of the two objects
r is the distance between the centers of the two objects

Calculating the Weight at a Height
Weight is a measure of the gravitational force acting on an object. On the Earth's surface, weight is equal to the product of an object's mass and the acceleration due to gravity (approximately 9.8 m/s^2).

Given that the child weighs 160N on the Earth's surface, we can calculate the mass of the child using the formula:

Weight = mass * acceleration due to gravity

160N = mass * 9.8 m/s^2

Solving for mass, we find:

mass = 160N / 9.8 m/s^2

Now, to calculate the weight of the child at a height of 3.6 × 10^6 m from the Earth's surface, we need to adjust the gravitational force equation by considering the distance from the center of the Earth.

Calculating the Distance
The distance from the Earth's surface to a height of 3.6 × 10^6 m can be calculated by subtracting the radius of the Earth from the total distance:

Distance = Total distance - Radius of the Earth

Distance = 3.6 × 10^6 m - 6.4 × 10^6 m

Calculating the Weight
Using the adjusted distance, we can calculate the weight of the child at the given height using the gravitational force equation:

Weight = G * (mass of the child * mass of the Earth) / (Distance from the center of the Earth)^2

Substituting the values into the equation, we can calculate the weight of the child at the given height.

Remember to calculate the mass of the Earth using its radius, density, and volume.