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Suppose the first stage of a two stage rocket has total mass $12,000 \mathrm{kg}$ , of which 9000 $\mathrm{kg}$ is fuel. The total mass of the second stage is $1000 \mathrm{kg},$ of which 700 $\mathrm{kg}$ is fuel. Assume that the relative speed $\boldsymbol{U}_{\mathbf{e x}}$ of ejected material is constant, and ignore any effect of gravity. (The effect of gravity is small during the firing period if the rate of fuel consumption is large) (a) Suppose the entire fuel supply carried by the two-stage rocket is utilized in a single-stage rocket with the same total mass of $13,000 \mathrm{kg}$ . In terms of $v_{e x}$ what is the speed of the rocket, starting from rest, when its fuel is exhausted? (b) For the two-stage rocket, what is the speed when the fuel of the first stage is exhausted if the first stage carries the second stage with it to this point? This speed then becomes the initial speed of the second stage. At this point, the second stage separates from the first stage.(c) What is the final speed of the second stage? (d) What value of $v_{\mathrm{ex}}$ is required to give the second stage of the rocket a speed of 7.00 $\mathrm{km} / \mathrm{s}$ ?

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(a) $v=1.37 v_{e x}$(b) $v_{1}=1.18 v_{\mathrm{ex}}$(c) $v_{2}=2.38 \mathrm{vex}$(d) $v_{e x}=2.94 \mathrm{km} / \mathrm{s}$

Physics 101 Mechanics

Chapter 8

Momentum, Impulse, and Collisions

Moment, Impulse, and Collisions

University of Michigan - Ann Arbor

University of Washington

Simon Fraser University

University of Sheffield

Lectures

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.

03:30

In physics, impulse is the integral of a force, F, over the time interval, t, for which it acts. Given a force, F, applied for a time, t, the resulting change in momentum, p, is equal to the impulse, I. Impulse applied to a mass, m, is also equal to the change in the object's kinetic energy, T, as a result of the force acting on it.

05:39

A Multistage Rocket. Suppo…

03:00

A small single-stage rocke…

03:55

A 2540-kg test rocket is l…

04:56

A $2540 \mathrm{~kg}$ test…

04:36

A 2540 -kg test rocket is …

06:58

The last stage of a rocket…

02:51

The second stage of a two-…

08:38

A small $8.00 \mathrm{~kg}…

14:46

A small 8.00-kg rocket bur…

06:33

A two-stage rocket is fire…

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