Randall D. Knight — Newton's Third Law: Problem Problem_50

A rocket burns fuel at a rate of \( 5.0 \text{ kg/s} \), expelling the exhaust gases at a speed of \( 4.0 \text{ km/s} \) relative to the rocket. We would like to find the thrust of the rocket engine. a. Model the fuel burning as a steady ejection of small pellets, each with the small mass \( \Delta m \). Suppose it takes a short time \( \Delta t \) to accelerate a pellet (at constant acceleration) to the exhaust speed \( v_{\text{ex}} \). Further, suppose the rocket is clamped down so that it can’t recoil. Find an expression for the magnitude of the force that one pellet exerts on the rocket during the short time while the pellet is being expelled. b. If the rocket is moving, \( v_{\text{ex}} \) is no longer the pellet’s speed through space but it is still the pellet’s speed relative to the rocket. By considering the limiting case of \( \Delta m \) and \( \Delta t \) approaching zero, in which case the rocket is now burning fuel continuously, calculate the rocket thrust for the values given above.