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 ✕ 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

(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