A model rocket with an initial mass of 2.0 kg is launched horizontally by burning and expelling 980 g of fuel with a velocity of 140 m/s. What is the velocity of the rocket after the fuel is expelled?
To solve this problem, we can use the principle of conservation of momentum. The total momentum before the fuel is expelled is equal to the total momentum after the fuel is expelled.
Before the fuel is expelled:
Initial mass of the rocket = 2.0 kg
Velocity of the rocket before the fuel is expelled = 0 m/s (since it is initially at rest)
After the fuel is expelled:
Mass of the rocket (after expelling fuel) = 2.0 kg + 0.98 kg (mass of expelled fuel) = 2.98 kg
Velocity of the rocket (after expelling fuel) = ?
The total initial momentum of the system is given by:
Total initial momentum = (mass of rocket before expelling fuel * velocity of rocket before expelling fuel) + (mass of expelled fuel * velocity of expelled fuel)
Since the rocket is initially at rest, the first term becomes 0, so we have:
Total initial momentum = (0) + (0.98 kg * 140 m/s) = 137.2 kg*m/s
According to the conservation of momentum, the total final momentum must also be equal to 137.2 kg*m/s.
The final momentum of the system after the fuel is expelled is given by:
Total final momentum = (mass of rocket after expelling fuel * velocity of rocket after expelling fuel)
We can rearrange this equation to solve for the velocity of the rocket after the fuel is expelled:
Velocity of rocket after expelling fuel = Total final momentum / mass of rocket after expelling fuel
Substituting the known values:
Velocity of rocket after expelling fuel = 137.2 kg*m/s / 2.98 kg
Simplifying:
Velocity of rocket after expelling fuel = 46.0 m/s
Therefore, the velocity of the rocket after the fuel is expelled is 46.0 m/s.