In certain cases, using both the momentum principle and energy principle to anal
ID: 1777599 • Letter: I
Question
In certain cases, using both the momentum principle and energy principle to analyze a system is useful, as they each can reveal different information. You will use the both momentum principle and the energy principle in this problem. A satellite of mass 2500 kg orbits the Earth in a circular orbit of radius of 7.1 x 106 m (this is above the Earth's atmosphere).The mass of the Earth is 6.0 x 1o24 kg. What is the magnitude of the gravitational force on the satellite due to the earth? F= 19847.25 N Using the momentum principle, find the speed of the satellite in orbit. (HINT: Think about the components of dp/dt parallel and perpendicular to P.) m/s Using the energy principle, find the minimum amount of work needed to move the satellite from this orbit to a location very far away from the Earth. (You can think of this energy as being supplied by work due to something outside of the system of the Earth and the satellite.) workExplanation / Answer
Given
mass of satellite m1=2500 kg, orbiting the Earth in a circular orbit of radius R = 7.1*10^6 m
mass of the Earth is m2= 6*10^24 kg ,
the magnitude of the gravitational force on the satellite is F = G*m1*m2/r^2
F = (6.67*10^-11*2500*6*10^24)/(7.1*10^6)^2 N
F = 19847.25 N
we know that the rate of change of momentum is force so
the force acting on it is the centripetal force
F = mv^2/r
v = sqrt(F*r/m)
v = sqrt(19847.25*7.1*10^6/2500) m/s
v = 7507.742 m/s
work done = change in kinetic energy
to move the satellite very far away from the Earth so that the gravitaional force on it would be zero results the speed of satellite is zero there
work = 0.5*m(v2^2-v1^2)
= 0.5*2500(0-7507.742^2) J
= -70457737423.2 J
-ve sign is work done on the satellite against the gravitational force of attraction of the Earth.
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