How much energy is required to move a 900 kg object from the Earth's surface to an altitude twice the Earth's radius?
To calculate the energy required to move a 900 kg object from the Earth's surface to an altitude twice the Earth's radius, we can use the following equation:
E = m * g * h
where:
E = energy (in joules)
m = mass of the object (in kg)
g = acceleration due to gravity (approximately 9.8 m/s^2)
h = height or altitude (in meters)
First, we need to determine the distance between the Earth's surface and an altitude twice the Earth's radius.
The radius of the Earth, denoted as "R," is approximately 6,371 km (or 6,371,000 meters). Twice the Earth's radius would be 2*R, which is 12,742 km (or 12,742,000 meters).
Next, we can calculate the difference in height (h) between the Earth's surface and the desired altitude:
h = (2 * R) - R = R
Therefore, the height or altitude (h) is equal to the Earth's radius.
Now, we can calculate the energy required:
E = m * g * h
E = 900 kg * 9.8 m/s^2 * 6,371,000 m
E = 5.52794 × 10^10 joules
Therefore, approximately 55.2794 billion joules of energy are required to move a 900 kg object from the Earth's surface to an altitude twice the Earth's radius.
To find out how much energy is required to move a 900 kg object from the Earth's surface to an altitude twice the Earth's radius, we need to consider the potential energy involved in the process.
The potential energy of an object can be calculated using the formula:
Potential Energy = Mass * Gravity * Height
In this case, the mass of the object is 900 kg, and the height we want to calculate is the distance from the Earth's surface to an altitude twice the Earth's radius.
The radius of the Earth is roughly 6,371 kilometers (or 6,371,000 meters). So, twice the Earth's radius would be 2 * 6,371,000 meters = 12,742,000 meters.
Now, let's consider the value of gravity. The gravitational acceleration on the Earth's surface is approximately 9.8 meters per second squared (m/s^2).
Using these values, we can calculate the potential energy:
Potential Energy = Mass * Gravity * Height
= 900 kg * 9.8 m/s^2 * 12,742,000 meters
Calculating this gives us the answer to the question:
Potential Energy = 1.075 x 10^11 joules
Therefore, approximately 1.075 x 10^11 joules of energy would be required to move a 900 kg object from the Earth's surface to an altitude twice the Earth's radius.
The potential energy increase is:
W = - M m G/(2R) + M m G/R
where M is the mass of the Earth, m is the mass of the object and R is the Earth's radius and G is the gravitational constant.
We can simplify the expression for W:
W = 1/2 M m G/R = m R/2 (M G /R^2) =
m R/2 g = 2.82*10^10 J