I'm having trouble setting up/solving this physics problem? Can someone please help me? Thank you.
A 4700 kg lunar lander is in orbit 45 km above the surface of the moon. It needs to move out to a 340-km-high orbit in order to link up with the mother ship that will take the astronauts home. How much work must the thrusters do?
change PE= min work
min work= GMm/r1-GMm/R2
M mass of moon, m is mass of lunar
To solve this physics problem, we can use the concepts of gravitational potential energy and work done. The work done is equal to the change in gravitational potential energy.
To calculate the work done, we need to find the change in gravitational potential energy. The change in gravitational potential energy (ΔPE) is given by the formula:
ΔPE = mgh
Where m is the mass, g is the acceleration due to gravity, and h is the change in height.
First, we need to find the gravitational potential energy at the initial orbit. The mass of the lunar lander is given as 4700 kg. The acceleration due to gravity on the moon is approximately 1.6 m/s^2. The initial height is 45 km, which we need to convert to meters.
1 km = 1000 m
So, 45 km = 45,000 m.
Now we can calculate the initial gravitational potential energy using the formula ΔPE = mgh:
ΔPE = (4700 kg) * (1.6 m/s^2) * (45,000 m)
Next, we need to find the gravitational potential energy at the final orbit. The final height is given as 340 km, which we need to convert to meters as well (1 km = 1000 m).
ΔPE = (4700 kg) * (1.6 m/s^2) * (340,000 m)
To find the work done, we subtract the initial gravitational potential energy from the final gravitational potential energy:
Work Done = ΔPE (final) - ΔPE (initial)
Finally, we can calculate the work done by subtracting the initial gravitational potential energy from the final gravitational potential energy:
Work Done = [(4700 kg) * (1.6 m/s^2) * (340,000 m)] - [(4700 kg) * (1.6 m/s^2) * (45,000 m)]
Simplifying the equation will give us the answer for the amount of work the thrusters must do.