Impulse and Momentum of a rocket

[Isquarey]

Homework Statement

Small model rocketry engines are sized by specific impulse. One common size is a C6 engine. With each letter increase in engine size. The "C" engine is 10.0 N -s specific impulse. The "6" indicates that the engine produces an average thrust of 6 Newtons.

How much time does the engine burn?

Homework Equations

P=mv
J=F*T
F*T=M(Vf-Vo)

The Attempt at a Solution

Just started this unit today worked through the rest 10 problems only one that i have no clue about.

 

[Isquarey]

My attemps were using all the equations posted and not making progress tried using kenimatics but don't have distance i think vo and vf is 0 but i know that's wrong because it would make it not move

 

[haruspex]

You are given an impulse and a force, and you want to determine a time. Which of the three equations you posted has such variables?

 

[collinsmark]

Homework Statement

Small model rocketry engines are sized by specific impulse. One common size is a C6 engine. With each letter increase in engine size. The "C" engine is 10.0 N -s specific impulse. The "6" indicates that the engine produces an average thrust of 6 Newtons.

How much time does the engine burn?

Homework Equations

P=mv
J=F*T
F*T=M(Vf-Vo)

The Attempt at a Solution

Just started this unit today worked through the rest 10 problems only one that i have no clue about.

I'm sorry if I'm about to confuse you, I must point out an inconsistency in the problem statement.

The problem statement gave the impulse as 10.0 N⋅s. Yet it called that "specific impulse." Both of those facts cannot be correct. I'm guessing that the problem statement should have said, "The 'C' engine is 10.0 N⋅s total impulse." There is a difference between total impulse and specific impulse.

Let me run some definitions by you:

Total impulse:
This is the average force of the engine times the amount of time the engine burns. This is the one that is consistent with your relevant equations. It has units of force times time, thus in the SI system, it has units of N⋅s (agrees with the problem statement, in-so-far as the units are concerned).

Specific impulse:
This is the impulse generated by one unit of fuel, divided by one unit amount of fuel. And now this one gets a little more complicated because you can express the unit "amount of" fuel in either mass or weight. If the unit amount of fuel is measured in terms of mass, then specific impulse has units of velocity (such as m/s). If the unit amount of fuel is measured in terms of weight, the specific impulse is expressed in units of time (such as seconds). Specific impulse is a good measure of how efficiently the engine uses fuel, but has no bearing on the total amount of fuel, or total amount of impulse.

Small model rocketry engines are typically specified according to their total impulse, not their specific impulse. This also agrees with the units given in the problem statement. So if I had to guess, cross out "specific" in the problem statement and replace it with "total."

[Edit: by the way, if the problem actually did mean specific impulse (albeit with wrong units), there isn't enough information to solve the problem. That's another indication that "total" impulse is what was intended to be written.]

 

[HalfLostAndSearching]

I would approach this problem by first defining impulse and momentum. Impulse is the change in momentum of an object, and momentum is the product of an object's mass and velocity. In the case of a rocket, the impulse and momentum are related to the force and time of the engine burn.

To determine the time of the engine burn, we can use the equation F*T = M(Vf-Vo), where F is the average thrust (in this case, 6 Newtons), T is the time of the engine burn, M is the mass of the rocket, Vf is the final velocity of the rocket, and Vo is the initial velocity of the rocket (assumed to be zero at launch).

We can also use the equation J = F*T, where J is the impulse and is equal to the change in momentum. We know that the specific impulse of the C6 engine is 10.0 N-s, which means that for every second the engine burns, it produces an impulse of 10.0 N-s.

To find the time of the engine burn, we can set these two equations equal to each other and solve for T:

F*T = M(Vf-Vo)
J = F*T
J = M(Vf-Vo)

10.0 N-s = M(Vf-Vo)

We can't solve for T without knowing the mass of the rocket and the final velocity, but we can make some assumptions. Let's assume that the rocket has a mass of 100 grams (0.1 kg), and the final velocity is 50 m/s. We can then solve for T:

10.0 N-s = (0.1 kg)(50 m/s - 0 m/s)
10.0 N-s = (0.1 kg)(50 m/s)
T = 0.2 seconds

So, for a rocket with a mass of 100 grams and a final velocity of 50 m/s, the C6 engine would burn for approximately 0.2 seconds. However, this time will vary depending on the mass and final velocity of the rocket.

In conclusion, the time of the engine burn can be determined by using the equations for impulse and momentum, and making assumptions about the mass and final velocity of the rocket.