A rocket engine consumes 450 kg of fuel per minute. If the exhaust speed of the ejected fuel is 5.2 km/s, what is the thrust of the rocket?
Thrust = v * dM/dt
Exhaust speed * rate of change of mass
450 kg/min / 60 s = 7.5 kg/s = change of mass over time
5.2 km/s * 1000 m = 5200 m/s = exhaust speed
(5200) (7.5) = 39000 N
39000 N / 1000 N = 39 kN
To calculate the thrust of the rocket, we need to use the equation:
Thrust = (Mass Flow Rate) x (Exhaust Speed)
Given:
Mass Flow Rate = 450 kg/min
Exhaust Speed = 5.2 km/s
First, we need to convert the mass flow rate from kg/min to kg/s:
Mass Flow Rate = 450 kg/min × (1 min/60 s) = 450/60 kg/s = 7.5 kg/s
Next, we convert the exhaust speed from km/s to m/s:
Exhaust Speed = 5.2 km/s × (1000 m/km) = 5200 m/s
Now we can calculate the thrust:
Thrust = Mass Flow Rate × Exhaust Speed
Thrust = 7.5 kg/s × 5200 m/s = 39,000 N
Therefore, the thrust of the rocket is 39,000 Newtons.
To calculate the thrust of the rocket, we can use the following formula:
Thrust = (Mass flow rate of fuel) × (Exhaust speed of fuel)
Given:
Mass flow rate of fuel = 450 kg/min
Exhaust speed of fuel = 5.2 km/s
However, to ensure our units are consistent, we need to convert the exhaust speed from km/s to m/s.
1 km = 1000 m
1 s = 1000 ms
Therefore, the exhaust speed of the fuel should be:
5.2 km/s × (1000 m/km) / (1000 ms/s) = 5200 m/s
Now we can plug the values into the formula:
Thrust = (Mass flow rate of fuel) × (Exhaust speed of fuel)
Thrust = 450 kg/min × 5200 m/s
However, we need to convert the mass flow rate from minutes to seconds. Since there are 60 seconds in a minute, we divide the mass flow rate by 60:
Thrust = (450 kg/min ÷ 60 s/min) × 5200 m/s
Now we can calculate the thrust:
Thrust = (7.5 kg/s) × (5200 m/s)
Thrust = 39,000 N
Therefore, the thrust of the rocket is 39,000 Newtons.