A model rocket with an initial mass of 2.0 kg is launched horizontally by burning and expelling 550 g of fuel with a velocity of 130 m/s. What is the velocity of the rocket after the fuel is expelled? (Assume the propellant is expelled instantaneously.)
To solve this problem, we can use the principle of conservation of momentum. The initial momentum of the rocket and fuel system is equal to the final momentum of the rocket after the fuel is expelled.
The initial momentum (before the fuel is expelled) is given by:
Initial momentum = (initial mass of the rocket and fuel system) * (initial velocity of the rocket and fuel system)
The final momentum (after the fuel is expelled) is given by:
Final momentum = (final mass of the rocket) * (final velocity of the rocket)
Using the principle of conservation of momentum, we can equate the initial momentum to the final momentum:
Initial momentum = Final momentum
(initial mass of the rocket and fuel system) * (initial velocity of the rocket and fuel system) = (final mass of the rocket) * (final velocity of the rocket)
We can rearrange this equation to solve for the final velocity of the rocket after the fuel is expelled:
Final velocity of the rocket = (initial mass of the rocket and fuel system) * (initial velocity of the rocket and fuel system) / (final mass of the rocket)
Given:
Initial mass of the rocket and fuel system = 2.0 kg
Initial velocity of the rocket and fuel system = 130 m/s
Mass of the fuel expelled = 550 g = 0.55 kg
Finding the final mass of the rocket:
Final mass of the rocket = (initial mass of the rocket and fuel system) - (mass of the fuel expelled)
Final mass of the rocket = 2.0 kg - 0.55 kg = 1.45 kg
Plugging in the values:
Final velocity of the rocket = (2.0 kg) * (130 m/s) / (1.45 kg)
Final velocity of the rocket = 260 kg m/s / 1.45 kg
Final velocity of the rocket ≈ 179.31 m/s
Therefore, the velocity of the rocket after the fuel is expelled is approximately 179.31 m/s.