(a) Taking the potential energy to be zero at infinite
separation, find the potential energy of a 30 kg object at the
surface of the Earth. (Use 6.37 ✕ 106 m for the Earth's
radius.)
________________J
(b) Find the potential energy of the same object at a height above
the Earth's surface equal to the Earth's radius.
_______________J
(c) Find the escape speed for a body projected from this
height.
__________________km/s
a)
Here is the formula for Gravitational Potential Energy
Ug = -GMm/r
Ug = - GMm/(R+h)
We plug given values,
Ug = - [(6.67*10^-11*5.9*10^24*30)/(6.37*10^6+ 0)
Calculating,
Ug = -1.85*10^9 J
b)
Now here h=R
Ug = - GMm/(R+h)
Ug = - [(6.67*10^-11*5.9*10^24*30)/(6.37*10^6+ 6.37*10^6)
Calculating,
Ug = -9.27*10^8 J
c)
To determine the escape velocity from this distance we just recall the usual method setting KE + PE = 0
1/2mv^2 = GMm/r
1/2,mv^2 = 9.27*10^8
1/2*30*v^2 = 9.27*10^8
v= 7.8*10^3 m/s = 7.8km/s
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