Hi I\'m looking for help doing the work to these questions. I had the answers gi
ID: 1474805 • Letter: H
Question
Hi I'm looking for help doing the work to these questions. I had the answers given to me but I couldn't understand the methods of solving. Thanks for the help.
Problem 1:
a.) Find the launch velocity needed to launch a projectile to a height of R (radius of the Earth) above the Earth's crust.
Answer: 7,900 m/s
b.) Find the minimum velocity to launch and escape the Earth completely.
Answer: 1.12 x 10^4 m/s
Problem 2:
A satellite with a mass of 1000 kg is put into orbit 300 km above the Earth.
a.) What is its speed, period, and acceleration?
Answers: 7,720 m/s, 5,440 s, 8.92 m/s^2
b.) How much work is done to put it in orbit?
Answer: 3.26 x 10^10 J
c.) How much work is needed for it to escape completely?
Answer: 2.98 x 10^10 J
Here are useful constants to know:
Newton's Gravitational constant, G = 6.67 x 10^(-11) N*m^2/kg^2
Radius of the Earth, R = 6.38 x 10^6 m
Mass of the Earth, M = 5.97 x 10^24 kg
Here are useful equations to know:
U=-GMm/r (Potential Energy)
v=sqrt(GM/r) (Velocity)
T=2pi*r/v (Period)
a=v^2/r (Acceleration
Explanation / Answer
Problem 1:
Accleration due to gravity g =9.8m/s^2
Radius of earth R =6371 km
Orbital speed vo = [gR]^1/2 = [9.8*6371*1000]^1/2
vo = 7900 m/s
b) ve = (vo)(2)^1/2 = 1.414*7900
ve = 1.12x10^4 m/s
Problem 2:
Mass of earth M =5.98x10^24 kg
G =6.67x10^-11 N.m^2/kg^2, h = 300 km
v= [GM/(R+h)]^1/2
= [(6.67x10^-11x5.98x10^24)/(6671x1000)]^1/2
v = 7720 m/s
V =2pi(R+h)/T
T = (2x3.14x6671x1000)/7720
Time period T = 5440 s
a =GM/(R+h)^2 =(6.67x10^-11x5.98x10^24)/(6671x1000)^2
a =8.92 m/s^2
(b) m = 1000 kg
W = (GMm/R) -(1/2)mv^2
W = [6.67x10^-11x5.98x10^24)/(6371x1000)] - (0.5*1000*7720*7720)
W = 3.26x10^10 J
(c) m =1000 kg
W = change in kinetic energy = (1/2)mv^2
W =(0.5*1000*7720*7720)
W = 2.98x10^10 J
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