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 an object from the Earth's surface to an altitude twice the Earth's radius, we need to consider the gravitational potential energy.
The gravitational potential energy (U) of an object at a certain altitude is given by the formula: U = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height.
At the Earth's surface, g is approximately 9.8 m/s^2. So, the potential energy (U1) of the object at the Earth's surface is: U1 = 900 kg * 9.8 m/s^2 * 1 Earth's radius.
To calculate the potential energy at an altitude twice the Earth's radius, we first need to find the value of h. Since the Earth's radius is denoted as R, the altitude twice the Earth's radius is 2R. The height h is the difference between the two altitudes, which is: h = 2R - R = R.
Now, we can calculate the potential energy (U2) at an altitude twice the Earth's radius: U2 = mgh = 900 kg * 9.8 m/s^2 * R.
To obtain the energy required to move the object to this altitude, we subtract the initial potential energy from the final potential energy: Energy required = U2 - U1 = 900 kg * 9.8 m/s^2 * R - 900 kg * 9.8 m/s^2 * 1 Earth's radius.
Finally, we can simplify the equation by substituting the value of the Earth's radius, which is approximately 6,371,000 meters: Energy required = 900 kg * 9.8 m/s^2 * 6,371,000 m * R - 900 kg * 9.8 m/s^2 * 6,371,000 m.
Note that the value of R depends on the units used, so this calculation can be done with either meters or kilometers, depending on the desired unit for the energy required.