WHEN WORLDS COLLIDE 5) Two heavenly bodies both with radi of 4x101 miles and mas
ID: 2269057 • Letter: W
Question
WHEN WORLDS COLLIDE 5) Two heavenly bodies both with radi of 4x101 miles and masses of 6x10 kg are separated by 3x10' miles. They are initially at rest. How fast are they moving just before their surfaces n the space between the planets Sam: arumern Last Awer: 784267 ms Answer: Not yet correct, tries 1/35 Hint: Consider the initial "scene" before the planets gain any spood and the final scene just when the surfaces are about to collide. What types of energy are relevant in each scene? Are the centers of the planets still separate in the final scene? Will that separation (if it exists) play a significant role? 6) Consider the same setup as before, only one planet is twice the mass of the other (their radii are still the same size). What is the speed of the more massive planet just before their surfaces collide? Submit All AnsawersExplanation / Answer
radius of the planet R = 4.0e+3 miles = 6.437 e+6 m
distance bteween the planets D = 3.0e+7 miles = 4.83e+10 m
Mass of each planet M = 6.0e+24 kg
D >> R and hence the PE when seperated by D is much smaller and can be ignored compared to when they are in contact and seperated by a distance of 2R, distance between their centers.
PE when they are in conatct = -GM2/2R,
we consider the PE as 0 when they are seperated by infinity or approx. 0 at D.
This is a reduction in PE and is equal to the gain in KE of the planets
Both palents will be moving towards each other , both being equal in mass both will have the same speed say V
KE of each planet = MV2/2
Total KE of the system = MV2
speed V = sqrt( GM/2R) = (6.67e-11 * 6.0e+24/2*6.437e+6)1/2
= 5575.5 m/s
b) let V is the speed of the heavier planet and v the speed of smaller plaent when they are just touching each other.
intial momentum of the system is 0
when thier surfaces just touch each other
2MV -Mv =0 , conserving the total momentum
V = v/2
Total KE of the system = MV2/2 + Mv2 /2 = 5MV2/2 = ( GM/2R)
speed of the massive planet V = (2*6.67e-11 * 6.0e+24/5*6.437e+6)1/2
= 4987 m/s
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