A spacecraft of mass 2000kg, moves at a constant speed of 7800m.s- in space. the main engine switched on for 10s during which time the exhaust gases travels at 10 000m.s-. As a result of this, the craft travels at 8000m.s- after 10s. Calculate the mass of the exhaust gas.
To calculate the mass of the exhaust gas, we can use the principle of conservation of momentum.
The momentum of an object can be calculated by multiplying its mass by its velocity. The total momentum before and after the engine is switched on should be the same, assuming no external forces act on the spacecraft.
Let's denote the mass of the spacecraft as M and the initial velocity of the spacecraft as V1. The mass of the exhaust gas can be denoted as m, and its velocity can be denoted as V2.
Before the engine is switched on, the momentum of the spacecraft is given by:
M * V1
After the engine is switched on, the momentum of the spacecraft can be calculated by considering the momentum of the exhaust gas and the change in momentum of the spacecraft. The momentum of the exhaust gas is given by:
m * V2
The change in momentum of the spacecraft is the difference between the final and initial momentum:
(M + m) * Vf - M * V1
Since the total momentum before and after the engine is switched on should be the same, we can set up the following equation:
M * V1 = (M + m) * Vf - m * V2
Given the following values:
M = 2000 kg
V1 = 7800 m/s
Vf = 8000 m/s
V2 = 10,000 m/s
We can substitute these values into the equation and solve for the unknown value m, which represents the mass of the exhaust gas.