Physic <span title="C............rocket!!!!!!!!!!!?">C............rocket!!!!!!...</span>

Question

The last stage of a rocket, which is traveling at a speed of 7600 m/s, consists of two parts that are clamped together: a rocket case with a mass of 290.0 kg and a payload capsule with a mass of 150.0 kg. When the clamp is released, a compressed spring causes the two parts to separate with a relative speed of 910.0 m/s. What are the speeds of (a) the rocket case and (b) the payload after they have separated? Assume that all velocities are along the same line. Find the total kinetic energy of the two parts (c) before and (d) after they separate. (e) Account for the difference.

Answer 1

Consider moving with the rocket so it appears at rest. When the spring does it&#039;s thing, it will impart equal and opposite momentums to each section of the rocket.

150*u = 290*v .... direction of v is opposite that of u

And we also know that: u + v = 910 m/s

150*u = 290*(910 - u)

440u = 290*910 = 263900

u = 599.77

v = 310.23

Speed of payload = 7600 + 599.77 = 8199.77

Speed of case = 7600 - 310.23 = 7289.77

kinetic energy before = (1/2)(440)(7600)^2 = 12707200000 J

kinetic energy capsule (after) = (1/2)(150)(8199.77)^2 = 5042717104 J

kinetic energy case (after) = (1/2)(290)(7289.770^2 = 7705408265 J

Sum of both = 12748125369 J

Difference = 40925369 J

The additional energy is derived from the potential energy of the spring before the clamp is released.