A spherical asteroid has a radius of 585 km and a surface g of 10.0 m/s 2 . a.)

Question

A spherical asteroid has a radius of 585 km and a surface g of 10.0 m/s2.

a.) What is the mass of the asteroid?
kg

b.) What is the potential energy of a 1 kg object on the surface?
J

c.) What is the minimum speed at which an object* must be thrown upwards from the surface to never come back down?
m/s

d.) If a 1 kg object is thrown directly upwards from the surface with a speed of 1000 m/s,

i.) What is its initial kinetic energy upon launch?
J

ii.) How high will it go above the asteroid's surface*?
m

e.) If a 1 kg object is dropped from rest 1000 km above the planet's surface:

i.) What is its initial potential energy when dropped?
J

ii.) With what speed will the object hit the surface*?
m/s

Explanation / Answer

a) g = GM/R^2

10 = (6.67*10^-11*M)/(585000^2)

M = 5.13081e+22 Kg

b) PE = GMm/R = mg = 10 N

c) Vmin = sqrt(2*g*R) = 3.42053e+3 m/s

d)
i) KEi = (1/2)*m*V^2 = (1/2)*1*1000^2 = 5e+5 J

ii) KEi = GMm/(R+h)
h = 6.2595e+6m

e)

i) PE = GMm/(R+h) = 2.15915e+6 J

ii) 0.5*m*V^2 = PE

V = 2.07805e+3 m/s

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