T-Mobile 7:49 PM @ 71%- WHEN WORLDS COLLIDE 5) Two heavenly bodies both with rad

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T-Mobile 7:49 PM @ 71%- WHEN WORLDS COLLIDE 5) Two heavenly bodies both with radii of 6x103 miles and masses of 8x1024 kg are separated by 4x10 miles. They are initially at rest. How fast are they moving just before their surfaces collide. Assume that you can ignore any effects having to do with the existence of atmospheres and that nothing significant exists in the space between the planets. Answer: 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? Answer: 7) A mad scientist wants to design a mechanical spring that has the ability to launch a 3 metric ton payload into deep space. Assuming that the spring's maximum compression is 250 m, what would its stiffness have to be to successfully launch such a payload? [Note that the mass of the Earth is about 6 x 10kg and its radius is about 6.4x 10 meters.] Answer: 8) If mad scientist invents a new material that is twice as stiff as the material in the previous problem, what speed will the payload have when it is very far away from the Earth, assuming a compression equal to the one in the previous problem? Answer: 9) You want to determine the stiffness constant of a spring in the physics lab. You attach one end of the spring to a hook that lets it dangle downward. On the other end of the spring you attach a 400 gram weight. You keep holding the weight, but lower it down until the spring reaches a stretch of 3 cm. At this point you feel a slight resistance to stretching the spring any further. When you release the weight, it hangs stably in its position. What is the stiffness constant of the spring? Answer 10) Which combination of statements is most accurate? [Enter your answer as a string of the letter options you believe are correct. For instance, if you think options A, D, and E are correct, then enter "ADE. NOTE: There are only 5 tries for this problem. A) Thermal energy is the same as temperature, they just use different units. B) Thermal energy changes during irreversible processes. C) Energy is not conserved by irreversible processes in an isolated system. D) Transformations of kinetic into potential energy are irreversible. E) None of the above Answer:

Explanation / Answer

Solution :-

a)let the speed of one body be x and the speed of other body be y.

Applying law of conservation of momentum,

M1*x = M2*y

since M1=M2,

x = y

Also,

applying law of conservation of energy,

loss in potential energy = gain in kinetic energy.

or -G*M1*M2/D + G*M1*M2/(R1+R2) = 0.5*M1*x^2 + 0.5*M2*y^2

or (-6.67*10^-11/(1.609*4*10^7) + 6.67*10^-11/(1.609*6*10^3*2))*8*10^24 = 0.5*x^2 + 0.5*y^2

using the two equations,

we get x=y=2.352*10^5 m/s

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