Rocket thrust, mass, speed given initial m and fuel consumption rate?

In summary, a rocket with a mass of 59.5E5 kg and 7.39E5 kg of fuel initially at rest in deep space, has a thrust of F=ma and a mass of 5.81E6 kg after firing its engine for 300 s at a fuel consumption rate of 480 kg/s. To find the rocket's thrust, the momentum integral ∫Fdt = Δp or the formula for calculating thrust in a variable mass system using mass rejection can be used. After the 300 s firing, the rocket's mass is 5.81E6 kg and its speed can be calculated using the rocket equation.
  • #1
rockchalk1312
38
0
A rocket, which is in deep space and initially at rest relative to an inertial reference frame, has a mass of 59.5E5 kg, of which 7.39E5 kg is fuel. The rocket engine is then fired for 300 s, during which fuel is consumed at the rate of 480 kg/s. The speed of the exhaust products relative to the rocket is 3.55 km/s.
(a) What is the rocket's thrust? After the 300 s firing, what are (b) the mass and (c) the speed of the rocket?

F=ma

Found mass by doing (300s)(480kg/s)=144000kg
Subtracted from 59.5E5-144000=5.81E6 kg

But I have no idea where to start on a and c. Thank you!
 
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  • #2
A hint for question a). Think about the units in Newtons equation..

Force = mass * acceleration

The units are..

= Kg * m/s^2

rearrange that a bit.
 
  • #3
rockchalk1312 said:
A rocket, which is in deep space and initially at rest relative to an inertial reference frame, has a mass of 59.5E5 kg, of which 7.39E5 kg is fuel. The rocket engine is then fired for 300 s, during which fuel is consumed at the rate of 480 kg/s. The speed of the exhaust products relative to the rocket is 3.55 km/s.
(a) What is the rocket's thrust? After the 300 s firing, what are (b) the mass and (c) the speed of the rocket?

F=ma

Found mass by doing (300s)(480kg/s)=144000kg
Subtracted from 59.5E5-144000=5.81E6 kg

But I have no idea where to start on a and c. Thank you!

I would use the momentum integral: ∫Fdt = Δp.
 
  • #4
rude man said:
I would use the momentum integral: ∫Fdt = Δp.

And I would use a direct formula for calculating thrust in a variable mass system: Mass rejection... :-p
 
  • #5
sankalpmittal said:
And I would use a direct formula for calculating thrust in a variable mass system: Mass rejection... :-p

Chaqu'un a son gout ...
 

Related to Rocket thrust, mass, speed given initial m and fuel consumption rate?

1. What is rocket thrust and how does it work?

Rocket thrust is the force that propels a rocket forward. It is generated by the engine pushing hot gases out of the back of the rocket at high speed. According to Newton's third law of motion, for every action, there is an equal and opposite reaction. This means that the force of the gases pushing out of the rocket is also pushing the rocket in the opposite direction, creating thrust.

2. How is rocket mass related to its speed and fuel consumption rate?

The mass of a rocket has a direct impact on its speed and fuel consumption rate. As the rocket consumes fuel, its mass decreases, which allows it to accelerate faster due to the decrease in weight. However, as the rocket's mass decreases, its fuel consumption rate also increases, as there is less mass to be propelled forward. This relationship is known as the rocket equation, which states that the change in velocity is directly proportional to the logarithm of the initial mass of the rocket divided by its final mass.

3. How does the initial mass of a rocket affect its speed and fuel consumption rate?

The initial mass of a rocket is a crucial factor in determining its speed and fuel consumption rate. A higher initial mass means that the rocket will have more fuel to consume, allowing it to maintain a higher speed for a longer period. However, a higher initial mass also means that the rocket will be heavier, making it more difficult to accelerate and increasing its fuel consumption rate. Therefore, there is a trade-off between initial mass, speed, and fuel consumption rate in rocket design.

4. What is the relationship between rocket thrust and its fuel consumption rate?

Rocket thrust and fuel consumption rate are inversely related. This means that as the thrust increases, the fuel consumption rate decreases, and vice versa. This relationship is due to the rocket's engine design and the amount of fuel being consumed at a certain rate to generate the necessary thrust for the rocket to reach and maintain its desired speed.

5. How do different types of fuel affect rocket thrust and speed?

The type of fuel used in a rocket can have a significant impact on its thrust and speed. Generally, rocket fuels are classified as either solid or liquid. Solid fuels tend to have a higher thrust but a lower specific impulse (a measure of efficiency), while liquid fuels have a lower thrust but a higher specific impulse. The type of fuel used also affects the weight and complexity of the rocket, which can further impact its speed and thrust capabilities.

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