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MOMENTUM

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The linear momentum of a particle or an object thatcan be modeled as a particle of mass (m) movingwith a velocity (v) is defined to be the product of themass and velocity:

p=mv

The impulse of the force F acting on a particle equalsthe change in the momentum of the particle.

Ft=m∆𝒗

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CONSERVATION OF MOMENTUM

Conservation of momentum is a fundamentallaw of physics which states that themomentum of a system is constant if thereare no external forces acting on the system. Itis embodied in Newton's first law (the law ofinertia). SCIENCEWORLD

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Conservation of Momentum for a System of Objects Internal forces have absolutely no effect on the net

momentum of a system. If the net external force acting on a system is zero, its

net momentum is conserved. That is,

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COEFFICIENT OF RESTITUTIONHow much bounce!

The ration between the relative speeds

𝒆 =𝒗𝟐′ − 𝒗𝟏

′

𝒗𝟏 − 𝒗𝟐

Perfectly elastic 𝒆 = 𝟏, perfectly inelastic 𝒆 = 𝟎, 𝒗𝟐′ = 𝒗𝟏

′

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A tennis ball dropped on the floor from a heightof 100 cm rebounds to a height of 60 cm. Findthe coefficient of restitution.

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Center of Mass

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

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Suppose the masses are separated by 0.500 m, and thatm1 = 0.260 kg and m2=0.170 kg. What is the distance fromm1 to the center of mass of the system?

𝑥𝑐𝑚 =𝑚1𝑥1 +𝑚2𝑥2

𝑚1 +𝑚2

=0.260 0 + 0.170(.500)

0.260 + 0.170= 0.198 𝑚

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A person’s arm is held with the upper arm vertical, the lower arm and hand horizontal. (a) Findthe center of mass of the arm in this configuration, given the following data: The upper arm hasa mass of 2.5 kg and a center of mass 0.18 m above the elbow; the lower arm has a mass of 1.6kg and a center of mass 0.12 m to the right of the elbow; the hand has a mass of 0.64 kg and acenter of mass 0.40 m to the right of the elbow. (b) A 0.14-kg baseball is placed on the palm ofthe hand. If the diameter of the ball is 7.4 cm, find the center of mass of the arm–ball system.

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A 59-kg woman and a 71-kg man sit on a seesaw, 3.5 mlong. Where is their center of mass?

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A uniform carpenter's square has the shape of an L, asshown in the figure. Locate the center of mass relativeto the origin of the coordinate system.

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