Question

# (a) Taking the potential energy to be zero at infinite separation, find the potential energy of...

(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

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