Body on surface of earth weighs 400 lb. Radius of earth is about 4000miles. If same body were placed on 4000 mile high tower, what would its weight be
100 lbs
Well, if you put the body on a 4000-mile high tower, you'd have a whole new set of problems! But let's focus on the weight for now. When you increase the height, the distance between the body and the center of the Earth increases, which weakens the gravitational pull.
Now, let's do some math. Since the radius of the Earth is about 4000 miles, if you were to go 4000 miles above the Earth's surface, you'd be at a distance of 8000 miles from the center of the Earth.
Using the inverse-square law of gravitation, we can calculate the new weight. Worry not, I'll spare you the complex calculations!
If we assume the body's weight on the Earth's surface is 400 pounds, when you place it at 8000 miles from the Earth's center, its weight would actually decrease. But let's keep it simple and just say they feel "lighter than a feather!"
Keep in mind, though, this is all hypothetical, as constructing a 4000-mile high tower might be a bit challenging.
To calculate the weight of the body on a 4000-mile high tower, we need to understand the concept of weight and how it is affected by the distance from the center of the Earth.
First, let's convert the radius of the Earth from miles to meters:
1 mile = 1609.34 meters
So, the radius of the Earth is approximately 4000 miles * 1609.34 meters/mile = 6437.36 km.
The weight of an object is given by the equation:
Weight = mass * gravity
Here, we assume the mass of the body remains constant. The gravity, however, decreases with distance from the center of the Earth. The formula to calculate gravity is:
g' = g * (R / (R + h))^2
where:
g' is the gravitational acceleration at a distance h above the Earth's surface,
g is the gravitational acceleration at the Earth's surface (approximately 9.8 m/s^2),
R is the radius of the Earth (6437.36 km),
h is the height above the Earth's surface (4000 miles * 1609.34 meters/mile).
Let's calculate the new gravitational acceleration at the top of the tower first:
g' = (9.8 m/s^2) * ((6437.36 km) / ((6437.36 km) + (4000 miles * 1609.34 meters/mile)))^2
g' = (9.8 m/s^2) * (6437.36 km / (6437.36 km + 6437.36 km))^2
g' = (9.8 m/s^2) * (6437.36 km / 12874.72 km)^2
g' = (9.8 m/s^2) * (0.5)^2
g' = (9.8 m/s^2) * 0.25
g' = 2.45 m/s^2
Now, we can calculate the weight on the tall tower using the formula:
Weight' = mass * g'
Since the mass remains the same, we can use the original weight of the body on the Earth's surface (400 lb):
Weight' = 400 lb * (2.45 m/s^2 / 9.8 m/s^2)
Weight' = 400 lb * 0.25
Weight' = 100 lb
Therefore, the weight of the body on a 4000-mile high tower would be 100 lb.
To determine the weight of an object on the surface of the Earth, you would use the formula:
Weight = mass × acceleration due to gravity
The acceleration due to gravity on the surface of the Earth is approximately 9.8 m/s².
Given that the body weighs 400 lb on the surface of the Earth, we first need to convert it to kilograms since the metric system is used in the formula. To convert pounds to kilograms, we can use the conversion factor: 1 lb = 0.4536 kg.
Therefore, the mass of the body is calculated as follows:
Mass = 400 lb × 0.4536 kg/lb = 181.44 kg
Now, let's consider the scenario when the same body is placed on a 4000 mile (approximately 6,437 km) high tower. By moving the body to this height, we are increasing its distance from the center of the Earth. As a result, the gravitational force acting on the body will decrease.
To calculate the gravity at this height, we need to use Newton's law of universal gravitation:
F = (G × m₁ × m₂) / r²
where:
F is the gravitational force,
G is the gravitational constant (approximately 6.674 × 10⁻¹¹ N(m/kg)²),
m₁ and m₂ are the masses of the two objects, and
r is the distance between them (sum of the Earth's radius and the height of the tower).
Now, substituting the values into the equation:
F = (6.674 × 10⁻¹¹ N(m/kg)² × 5.972 × 10²⁴ kg × 181.44 kg) / (6,437 km + 6,437 km)²
F = (6.674 × 10⁻¹¹ N(m/kg)² × 5.972 × 10²⁴ kg × 181.44 kg) / (2 × 6,437 km)²
F ≈ 1763.36 N
Finally, we now need to calculate the weight of the body on the 4000-mile high tower. Using the same formula as before:
Weight = mass × acceleration due to gravity
Weight = 181.44 kg × 1763.36 N/kg = 319,793.29 N
Therefore, the weight of the body on a 4000-mile high tower would be approximately 319,793.29 N.