Question

3questions in total please
*Problem 6.66 You stand on a spherical asteroid of uniform density whose mass is 2.5 x 1016 kg and whose radius is 11 km (11 x 103 m). These are typical values for small asteroids, although some asteroids have been found to have much lower average density and are thought to be loose agglomerations of shattered rocks. You want to figure out how fast you have to throw the rock so that it never comes back to the asteroid and ends up traveling at a speed of 10 m/s when it is very far away. hav nt to

Answer 1

Given :

Mass of asteroid (M) = 2.5 ×10¹⁶ Kg

Radius of asteroid (R) = 11× 10³ m

Final velocity of rock (V) =10 m/s

Lets mass of rock is 'm'

As there is no external forces are acting So, the energy will be conserve therefore :

T.E_f = T.E_i

Lets final and initial kinetic energy of rock are K_f and K_i respectively

Similarly,

Final and initial potential energy of rock are P_f and P_i respectively.

So,

K_i + P_i = K_f + P_f

GmM

22GAM

2 × 6.674 × 10-11 × 2.5 × 1016 11000 +10

2 × 6.674 × 2.5 × 102 +102 V)

v= 20 m/s

So, initial speed of rock to not com back at asteroid is 20m/s

Now,

(a) As there is some final speed so the final kinetic energy is not ZERO

(b) Total energy of (rock + asteroid will be conserve so in both state Total energy will be EQUAL

(c) initially velocity is 20 m/s and final velocity is 10 m/s so final kinetic energy of rock is LESS than initially kinetic energy of rock

(d) As the velocities are of same order so change in kinetic energy is NOT NEGLIGIBLE

(e) As the final kinetic energy is less So to conserve the Total energy final potential energy will be MORE than the initial potential energy