Question

(a) Taking the potential energy to be zero at infinite
separation, find the potential energy of a 87 kg object at the
surface of the Earth. (Use 6.37 ✕ 10^{6} 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

(D) An object is projected upward from the surface of the Earth with an initial speed of 3.9 km/s. Find the maximum height it reaches.

_____________m

Answer #1

gravitational potential energy = -GMm / r

gravitational potential energy at surface= -6.648 * 10^-11 * 5.972 * 10^24 * 87 / (6.37 * 10^6)

**gravitational potential energy at surface energy =
5422388496.08 J**

gravitational potential energy at height R = -6.648 * 10^-11 * 5.972 * 10^24 * 87 / (2 * 6.37 * 10^6)

**gravitational potential energy at height R =
-2711194248.04 J**

escape velocity = sqrt(2GM / r)

escape velocity = sqrt(2 * 6.648 * 10^-11 * 5.972 * 10^24 / (2 * 6.37 * 10^6))

**escape velocity = 7894.701 m/s or 7.8947
km/s**

0.5 * 87 * 3900^2 = 6.648 * 10^-11 * 5.972 * 10^24 * 87 / (6.37 * 10^6 + h)

**d) h = 4.58349×10^7
m**

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