Rockets Momentum and Impulse Rocket Propulsion n In

Rockets Momentum and Impulse

Rocket Propulsion n In rockets fuel is burning at all times so we must include this decrease in mass. Exhaust A rocket fired in outer space

Velocity of the Rocket Momentum

At the end of time, t, the velocity has increased to (v + dv) and the mass has decreased to (m + dm) [dm is negative]. n The rocket’s momentum at this time (m + dm)(v + dv) n The x-component of momentum of the rocket and exhaust is as follows: n

Momentum for the Rocket

Continued

Rockets Effective rockets burn fuel at a large rate n That means dm/dt is large and it is a negative number so the acceleration is positive n If the velocity of the exhaust is constant then we integrate to find the relationship between v at any time and the mass. n

Integrate In rockets mo/m is very large.

Problem 1 n A rocket is in outer space, far from any planet, when the rocket engine is turned on. In the first second of firing, the rocket ejects 1/120 of its mass with a relative speed of 2400 m/s. What is the rocket’s initial acceleration?

Answer

Problem 2 n Suppose that ¾ of the initial mass mo of the rocket above is fuel, so the final mass is m=mo/4 and that the fuel is completely consumed at a constant rate in a total time t = 90 sec. If the rocket starts from rest, find its speed at the end of this time.

Answer