Space probes may be attached to their launchers by exploding bolts, which can be

Question

Space probes may be attached to their launchers by exploding bolts, which can be used to separate the parts after takeoff. Suppose a 4650 kg satellite uses this method to separate from the 1600 kg remains of its launcher, and that a total of 4950 J of energy is supplied to the two parts by the explosion. This process is "perfect" in the sense that the energy is transferred entirely to the motion of the system, rather than any deformations or other internal energy changes. What is the subsequent velocity, in meters per second. of the satellite, using the frame of reference in which they were at rest before separation? Assume the satellite will be moving in the positive direction after separation. V_1 = What is the subsequent velocity, in meters per second, of the launcher, using the frame of reference specified above?

Explanation / Answer

TOTAL MASS OF THE SYSTEM IS m = m1+m2 = 4650+1600 = 6250 Kg

Using law of conservation of energy

energy of the system before seperation = energy of the system after seperation

0 = 0.5*(m1+m2)*v^2 = 4950

0.5*6250*v^2 = 4950

v = 1.258 m/sec

Using law of conservation of momentum

0 = (m1*V1) + (m2*V2)

0 = (4650*1.258)+(1600*V2)

V2 = - 3.65 m/sec

negative shows that it was opposite to the motion of the satellite

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