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The second stage of a two-stage rocket weighs 2000 lb (empty) and is launched from the first stage with a velocity of $3000 \mathrm{mi} / \mathrm{h}$. The fuel in the second stage weighs 1000 Ib. If it is consumed at the rate of $50 \mathrm{lb} / \mathrm{s}$ and ejected with a relative velocity of 8000 ft/s, determine the acceleration of the second stage just after the engine is fired. What is the rocket's acceleration just before all the fuel is consumed? Neglect the effect of gravitation.

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Physics 101 Mechanics

Chapter 15

Kinetics of a Particle: Impulse and Momentum

Newton's Laws of Motion

Applying Newton's Laws

Moment, Impulse, and Collisions

University of Washington

Simon Fraser University

Hope College

University of Sheffield

Lectures

03:43

In physics, dynamics is the branch of physics concerned with the study of forces and their effect on matter, commonly in the context of motion. In everyday usage, "dynamics" usually refers to a set of laws that describe the motion of bodies under the action of a system of forces. The motion of a body is described by its position and its velocity as the time value varies. The science of dynamics can be subdivided into, Dynamics of a rigid body, which deals with the motion of a rigid body in the frame of reference where it is considered to be a rigid body. Dynamics of a continuum, which deals with the motion of a continuous system, in the frame of reference where the system is considered to be a continuum.

04:30

In classical mechanics, impulse is the integral of a force, F, over the time interval, t, for which it acts. In the case of a constant force, the resulting change in momentum is equal to the force itself, and the impulse is the change in momentum divided by the time during which the force acts. Impulse applied to an object produces an equivalent force to that of the object's mass multiplied by its velocity. In an inertial reference frame, an object that has no net force on it will continue at a constant velocity forever. In classical mechanics, the change in an object's motion, due to a force applied, is called its acceleration. The SI unit of measure for impulse is the newton second.

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in this problem. We have a two stage rocket with a given weight, and we know the rate in which fuel is being consumed and ejected. Now we need to determine declaration off the second stage of the rocket just after the Indian is fired and the rockets acceleration just before all the fuel is consumed. So in the initial case, just after the engines fired, we know that using the steady flow equations at the sum of all the forces acting on this rocket was equal to M D v D P minus the D E, which is the relative rate at which, if you are moving, I'm Yeah, the math floor it off dejected fueled the M E T T. So we know that if we assume that they waited negligible, there's no forces acting on the rocket. It's math is 2000 plus £1000 for the £3000 which is its weight over G 32.2 and DVD T is the acceleration of the rocket A. But this is minus 8000 feet, the second and a florid off £50 per second so that 50 divided by G convert that to a math. And so if you rearrange the equation, we get that the acceleration just after the engine is fired is 133 feet, the square second. That was initially now, finally, just before all the fuel is consumed, we use the steady flow equation again, and we have that the forces be some of the forces acting on the rocket, which is zero. Now all the fuel is consumed to the masses. Only that off the the rocket, which is £2000 over 32.2 times a Miami, 8000 until 50 over again, 32.2. And if you rearrange this, we get the information off the rocket finally to be 200 feet the square second.

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