Understanding Gravity and Weight
* Gravity: Gravity is the force of attraction between any two objects with mass. The more massive the objects, the stronger the gravitational force.
* Weight: Weight is the force of gravity acting on an object's mass. It's calculated using the formula: Weight (W) = Mass (m) * Acceleration due to gravity (g)
Key Concepts
* Inverse Square Law: The force of gravity decreases with the square of the distance between the centers of the objects. This means if you double the distance, the force becomes four times weaker.
* Earth's Radius: The Earth's average radius is approximately 6,371 kilometers (3,959 miles).
Calculations
1. Set up the problem: We want to find the height (h) where the weight (W') is half the weight on Earth (W):
* W' = 1/2 * W
2. Apply the inverse square law: Since weight is directly proportional to the force of gravity, the weight at height 'h' is inversely proportional to the square of the distance from the Earth's center:
* W' / W = (R / (R + h))^2
* Where R is the Earth's radius.
3. Substitute and solve for h:
* (1/2 * W) / W = (R / (R + h))^2
* 1/2 = (R / (R + h))^2
* √(1/2) = R / (R + h)
* (R + h) = R / √(1/2)
* h = R / √(1/2) - R
* h ≈ 0.414 * R
4. Plug in Earth's radius:
* h ≈ 0.414 * 6,371 km
* h ≈ 2640 km (approximately)
Answer
An object's weight would be half its weight on Earth at a height of approximately 2640 kilometers above the Earth's surface.
