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Two asteroids with masses $m_{A}$ and $m_{B}$ are moving with velocities $\vec{v}_{A}$ and $\vec{v}_{B}$ with respect to an astronomer in a space vehicle. (a) Show that the total kinetic energy as measured by the astronomer is$$K=\frac{1}{2} M v_{\mathrm{cm}}^{2}+\frac{1}{2}\left(m_{A} v_{A}^{\prime 2}+m_{B} v_{B}^{\prime 2}\right)$$with $\vec{v}_{\mathrm{cm}}$ and $M$ defined as in Section $8.5, \vec{v}_{\mathrm{A}}^{\prime}=\vec{v}_{\mathrm{A}}-\overrightarrow{\boldsymbol{v}}_{\mathrm{cm}},$ and $\vec{v}_{B}^{\prime}=\vec{b}_{B}-\vec{b}_{\mathrm{cm}},$ In this expression the total kinetic energy of the two asteroids is the energy associated with their center of mass plus the energy associated with the internal motion relative to the center of mass. (b) If the asteroids collide, what is the minimum possible kinetic energy they can have after the collision, as measured by the astronomer? Explain.

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a. $K=\frac{1}{2}\left(m_{A}+m_{B}\right) v_{\mathrm{em}}^{2}+\frac{1}{2}\left(m_{A} v_{A}^{\prime 2}+m_{B} v_{B}^{\prime 2}\right)+\left(m_{A} \overrightarrow{\boldsymbol{v}}_{A}^{\prime}+m_{B} \overrightarrow{\boldsymbol{v}}_{B}^{\prime}\right) \cdot \overrightarrow{\boldsymbol{v}}_{\mathrm{cm}}$b. $\frac{1}{2} M v_{\mathrm{cm}}^{2}$

Physics 101 Mechanics

Chapter 8

Momentum, Impulse, and Collisions

Moment, Impulse, and Collisions

University of Michigan - Ann Arbor

Simon Fraser University

Hope College

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.

07:25

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03:48

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02:31

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04:02

08:01

Two asteroids of equal mas…

31:20

Two hypothetical planets o…

03:12

03:10

Asteroid Collision. Two as…

03:08

Two spherical asteroids ha…

12:26

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