Rocket Propulsion Homework: Calculating Mass Loss R

[nns91]

Homework Statement

A Roadrunner F45 rocket engine, of mass 93g, is attached to a 2kg cylinder, which glides along a horizontal low friction nylon fishing wire. The thrust curve for the rocket engine is given.

In reality, 30g of propellant are burned as the engine is ignited. Calculate the average of mass loss R during burnout, in kg/s

Homework Equations

R= Ma/V_rel

The Attempt at a Solution

I guess Ma is the average thrust which I could calculate by using the graph. However, I don't know how to calculate V rel ( which is actually the next part of the problem). Is there any way I can calculate R other than use the normal formula ??

I have also calculated the impulse for the rocket.

 

[nns91]

Anyone found out about anything yet ??

I have been trying but still cannot find R without calculating Vrel

 

[thomate1]

The average thrust can be calculated by taking the area under the thrust curve, which is 360 Ns. To calculate the average mass loss, we need to find the average velocity of the exhaust gases and the average mass of gas expelled per unit time.

To find the average velocity of the exhaust gases, we can use the ideal gas law: PV=nRT. Since the engine is burning 30g of propellant, we can assume that the exhaust gases have a mass of 30g as well. We also know the temperature and pressure of the exhaust gases (since the engine is in a closed system), so we can solve for the volume of the gas.

Once we have the volume, we can calculate the average velocity using the equation V= d/t, where d is the distance traveled by the gas (which is the length of the engine) and t is the total burn time.

Next, we can calculate the average mass of gas expelled per unit time by using the equation m= PV/RT. This will give us the mass of gas expelled in one second.

Finally, we can plug these values into the equation R= Ma/Vrel to get the average mass loss during burnout in kg/s.

Overall, this problem requires us to use the ideal gas law and basic kinematic equations to calculate the average mass loss of the rocket engine during burnout. It also highlights the importance of understanding the properties and behavior of gases in rocket propulsion.