Answer to Question #271256 in Mechanical Engineering for jonathon

Question

A satellite launch vehicle travelling at 1000 m s −1 uses a controlled explosion to release its payload into orbit. The empty launch vehicle has a mass of 7500 kg and the satellite released has mass 250 kg. Both continue travelling in the same direction, with the launch vehicle now moving at 900 m s −1 . a) Calculate the initial momentum of the launch vehicle immediately before the satellite was released. b) Calculate the final velocity of the satellite after release.

Answer 1

a) The initial momentum of the launch vehicle immediately before the satellite was released

Initial momentum = Mu

Where u in initial velocity of launch vehicle before releasing satellite and

M is mass of launch vehicle with mass of satellite

Putting M=7750 kg and u=1000 m/s

Initial momentum = (7750 kg)(1000 m/s)

Initial momentum, P_i =7.750×10₆ kg•m/s

(b) The final velocity of the satellite after release can be determined by using momentum conservation.

Momentum conservation state that momentum before release of satellite is equall to momentum after release of satellite.

Momentum after release of satellite, P.F._f 

P_f = mv + m'v'       (1)

Where mass of empty launch vehicle, m=7500 kg

m' is mass of satellite , m'=250 kg

v is final velocity of launch vehicle after releasing satellite, v=900 m/s

v' is final velocity of the satellite after release

Putting all the values in equation (1), we get

P_f =(7500 kg)(900 m/s) + (250 kg)v'

P_f = 6.750×10⁶ kg•m/s + (250 kg)v'

Now applying conservation of momentum

Momentum before release of satellite = momentum after release of satellite

P_i = P_f

7.750×10₆ kg•m/s = 6.750×10⁶ kg•m/s + (250 kg)v'

(7.750×10₆ - 6.750×10⁶ )kg•m/s= (250 kg)v'

10⁶ m/s = 250v'

v' = (10⁶/250) m/s

v' = 4000 m/s

The final velocity of the satellite after release is 4000 m/s.