Physics 121C Mechanicsmorse/P170Af13-21.pdf · A 4.0 kg block moving to the right at 6.0 m/s undergoes an elastic head-on collision with a 2.0 kg block moving to the right at 3.0

Physics 170 - MechanicsLecture 21

Elastic Collisions and C.M.

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Elastic Collisions In elastic collisions, both kinetic energy and momentum are conserved.

One-dimensional elastic collision:

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Elastic Collisions in 1D

MomentumConservation

EnergyConservation

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Speed of approach = Speed of separation

Example:Elastic Collision of Two Blocks

A 4.0 kg block moving to the right at 6.0 m/s undergoes an elastic head-on collision with a 2.0 kg block moving to the right at 3.0 m/s.

Find their final velocities.

2D Elastic Collisions Two-dimensional collisions can only be solved if some of the final information is known, such as the final velocity of one object:

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Summary Collisions

Center of Mass The center of mass of a system is the point where the system can be balanced in a uniform gravitational field.

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Center of Mass For two objects:

The center of mass is closer to the more massive object.

Note that we can also apply this relation to the velocities and accelerations of the objects and their center of mass.

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Center of Mass The center of mass need not be within the object:

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Motion of the Center of Mass Motion of the center of mass:

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Center of Mass The center of mass is the point on (or near) an extended object that moves as if all the mass of the object were concentrated at that point.

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x2

Center of Mass The total mass multiplied by the acceleration of the center of mass is equal to the net external force:

The center of mass accelerates just as though it were a point particle of mass M acted on by

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Rocket Science

A rocket engine burns fuel and expels it from its exhaust as hot gases. The rocket+gas system is isolated and will have no change in momentum: pR + pG = 0

Therefore, the rocket gains momentum in the upward direction by giving momentum to the “fuel packet” that moves away at high velocity in the downward direction.

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Systems with Changing Mass:Rocket Propulsion

If a mass of fuel Δm is ejected from a rocket with speed v, the change in momentum of the rocket is:

The force, or thrust, is

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