Having aced your introductory physics course, you are hired as a summer intern a

Question

Having aced your introductory physics course, you are hired as a summer intern at NASA. You are sent as part of a team to explore the possibility of mining iron from a small, airless spherical asteroid with a radius of 502 km and a surface acceleration of 3.1 m/sec2.

1)

What is the mass of the asteroid?

kg

2)

What is the minimum vertical velocity you could give a 4 kg rock from the surface of this asteroid so that it continues to move upwards forever (i.e. it would never return to the surface)?

m/sec

3)

What is the minimum vertical velocity you could give a 8 kg rock from the surface of this asteroid so that it continues to move upwards forever (i.e. it would never return to the surface)?

m/sec

4)

How far will the 4 kg rock go if it leaves the asteroids surface with a vertical velocity of 1000 m/sec?";

m

5)

What will the speed of the 8 kg rock be at the surface of the asteroid if it is dropped from a point 1000km above the surface of the asteroid?

Explanation / Answer

(1) g=GM/R^2

M=g*R^2/G=1.17*10^22 Kg

(2)escape velocity=sqrt(2*g*R)=1764.2 m/s

(3)It will remain same i.e. 1764.2 m/s

(4)if v=1000 m/s

-GmM/502000+0.5*m*1000*1000=-GMm/502000+h

we got h=247456.3 m=247.5 km

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