A rocket burnt fuel av the rate of 20kgs^4 and eject it with a velocity of 5.0*10^3ms^-1. Calculate the thrust exerted by the gas on the rocket.
To calculate the thrust exerted by the gas on the rocket, we can use Newton's second law of motion, which states that force (F) is equal to the rate of change of momentum (dp/dt). In this case, the momentum change is caused by the ejection of gas at a certain velocity.
The formula for thrust is:
Thrust (F) = (dm/dt) * v
Where:
- (dm/dt) is the rate of change of mass (fuel consumption rate)
- v is the velocity of the ejected gas
Given:
- Fuel consumption rate (rate of change of mass) = 20 kg/s^4
- Velocity of ejected gas = 5.0 * 10^3 m/s^-1
Now, let's plug in these values into the formula to calculate the thrust:
F = (dm/dt) * v
F = 20 kg/s^4 * 5.0 * 10^3 m/s^-1
To simplify the units, we know that (1 s^-4 = 1 kg), so the units of dm/dt can be converted as follows:
F = 20 kg * 5.0 * 10^3 m/s^-1
F = 100,000 N
Therefore, the thrust exerted by the gas on the rocket is 100,000 Newtons (N).