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9.3 Conservation of momentum and Newton’s third law of motion
Example 6 Launching a space shuttle
At liftoff, a space shuttle
has an initial mass of
2.2  106 kg. When
launched, the rockets
and main engines expel
hot gas at a rate of
1.1  104 kg s1, with a
velocity of 2600 m s1.
(Take g = 10 m s2)
9.3 Conservation of momentum and Newton’s third law of motion
(a) Find the initial upward force acting on the
shuttle.
Rate of change momentum of the hot gas
mv  mu 1.1 10 4  2600  0


N
t
1
 2.86  107 N (downwards )
This is the force acting on the hot gas. By
Newton’s third law of motion, the thrust F’
acting on the rocket is 2.86  107 N in the
upward direction.
9.3 Conservation of momentum and Newton’s third law of motion
(b) Find the initial acceleration of the shuttle.
The net force F acting on the shuttle is given by
F = F’  mg
= (2.86  107  2.2  106  10) N
= 6.6  106 N
9.3 Conservation of momentum and Newton’s third law of motion
By Newton’s second law of motion,
F 6.6  106
2
2
a 
ms  3ms
6
m 2.2  10
The shuttle has an initial acceleration of 3 m s2.
Note that the acceleration of the shuttle will
increase with time. This is because the mass of
the shuttle will decrease when hot gas is being
expelled continuously.