The space shuttle is a spaceship which was designed for transporting a payload to near-earth orbits and to be used many times. When it stands on the launching pad, it consists of the orbiter itself, the external tank, and two booster rockets. The orbiter is 7.32 X 104 kg, while the whole assembly is 2.0 X 106 kg. The thrust at liftoff is 2.86 X 107 N, which is achieved by burning 3400 kg of fuel each second. The force provided by the engines is given by the product of the velocity of the exhaust gases relative to the ship and the rate (mass per time) at which fuel is burned.
As the space shuttle ascends, the rate of fuel burning is approximately constant, and so the mass of the shuttle decreases.
The following chart shows hypothetical data for the liftoff of a shuttle. We are assuming the shuttle moves in one dimension upward. Use 10 m/s2 for the acceleration due to gravity. The force due to gravity is Fgrav = Mg, where M is the mass of the object, and g is the acceleration due to gravity.
t(s) x (m) v (m/s)
0 0.0 x 104 0
90 2.0 x 104 490
180 9.6 x 104 1240
270 25.5 x 104 2400
What is the initial acceleration of the shuttle just as it begins leaving the launchpad?