Rocket Thrust Force Calculation

The force exerted on a rocket is called thrust. It arises from the momentum change of the expelled exhaust gases. The magnitude of this force can be calculated using the principle of momentum conservation.

Physics Principle

The thrust force ($F$) is equal to the rate at which momentum is carried away by the exhaust gases. Mathematically, this is expressed as:

$ F = \left| v_e \frac{dm}{dt} \right| $

Where:

• $v_e$ is the exhaust velocity of the gases.
• $\frac{dm}{dt}$ is the rate of fuel consumption (mass expelled per unit time).

Given Data

• Fuel consumption rate: $3000\text{ kg/min}$
• Exhaust speed ($v_e$): $5 \times 10^{3}\text{ m/s}$

Unit Conversion

The fuel consumption rate must be converted from kg/min to kg/s to be consistent with the SI unit of velocity (m/s).

$ \frac{dm}{dt} = \frac{3000\text{ kg}}{1\text{ min}} \times \frac{1\text{ min}}{60\text{ s}} = \frac{3000}{60}\text{ kg/s} = 50\text{ kg/s} $

Force Calculation

Now, substitute the values into the thrust formula:

$ F = (5 \times 10^{3}\text{ m/s}) \times (50\text{ kg/s}) $

$ F = 250 \times 10^{3}\text{ kg}\cdot\text{m/s}^2 $

Since $1\text{ N} = 1\text{ kg}\cdot\text{m/s}^2$, the force is:

$ F = 250 \times 10^{3}\text{ N} $

To express this in scientific notation similar to the options:

$ F = 25 \times 10^{1} \times 10^{3}\text{ N} = 25 \times 10^{4}\text{ N} $

Conclusion

The magnitude of the force exerted on the rocket is $25 \times 10^{4}\text{ N}$.