A satellite in a circular orbit around earth with a radius 1.019 times the mean radius of the earth is hit by an incoming meteorite. A large fragment m=60 kg is ejected in the backwards direction so that it is stationary with respect to the earth and falls directly to the ground. Its speed just before it hits the ground is 373 m/s.
A. Find the total work done by gravity on the satellite fragment.
B. Find the amount of that work converted to heat
To find the total work done by gravity on the satellite fragment, we can use the work-energy principle. The work done by gravity is equal to the change in kinetic energy of the satellite fragment.
A. The initial kinetic energy of the satellite fragment is zero since it was stationary. The final kinetic energy is given by the equation:
KE = (1/2)mv^2
where m is the mass of the fragment and v is the final velocity of the fragment. Substituting the given values, we have:
KE = (1/2)(60 kg)(373 m/s)^2
= 0.5 * 60 * (373)^2 J
= 651,210 J
Therefore, the total work done by gravity on the satellite fragment is 651,210 Joules.
B. To find the amount of work converted to heat, we need to know the initial potential energy of the fragment. The potential energy is due to the gravitational force acting on the fragment, and can be calculated using the formula:
PE = mgh
where m is the mass of the fragment, g is the acceleration due to gravity, and h is the change in height.
Since the fragment falls directly to the ground, the change in height is equal to the radius of the Earth. The radius of the Earth is not given, but we know that the radius of the satellite's orbit is 1.019 times the mean radius of the Earth.
Let's assume the mean radius of the Earth is r. Then, the change in height (h) is equal to (1.019r - r) = 0.019r.
Substituting the given values, we can calculate the potential energy:
PE = (60 kg)(9.8 m/s^2)(0.019r)
= 11.172r Joules
Therefore, the amount of work converted to heat is equal to the difference between the initial potential energy and the final kinetic energy:
Work converted to heat = PE - KE
= 11.172r J - 651,210 J
Please provide the value of the radius of the Earth or its mean value, so we can calculate the work converted to heat.