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Lecture OutlineChapter 6

College Physics, 7th EditionWilson / Buffa / Lou

Chapter 6Linear Momentum and

Collisions

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Linear MomentumImpulseConservation of Linear MomentumElastic and Inelastic CollisionsCenter of Mass

6.3 Conservation of Linear Momentum

• Remind me what momentum is...

• How do we calculate?

• Momentum is a very important part of collisions.

• As well as...

6.3 Conservation of Linear Momentum

Collisions happen quickly enough that any external forces can be ignored during the collision. Therefore, momentum is conserved during a collision.

What is a collision?

Isolated systems and only in one dimension

2 types of collisions The biggest differences between these collisions are: 1. 2.

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6.4 Elastic and Inelastic Collisions• Elastic Collisions:

• Total kinetic energy is conserved.

• Some or all initial kinetic energy is temporarily converted to potential as objects are deformed. After deformation, objects elastically "spring" back where system regains original KE.

6.4 Elastic and Inelastic Collisions• Inelastic Collisions:

• The total kinetic energy is not conserved.

• Where does energy go?

• One or more objects may not go back to their original shape.

• Everyday collisions are Inelastic.

6.4 Elastic and Inelastic Collisions

• For isolated systems, momentum is conserved for Elastic and Inelastic collisions.

• Pinitial = Pfinal

6.4 Elastic and Inelastic Collisions

Total kinetic energy is not conserved in an inelastic collision.

Total momentum before collision is same as after collisions.

In a completely Inelastic collision the objects stick together. (both objects will have same ......)

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6.4 Elastic and Inelastic Collisions

A completely inelastic collision is one where the objects stick together afterwards.

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6.4 Elastic and Inelastic Collisions• Mathematical equations for Inelastic

Collisions:

• For momentum

• m1v1i = (m1 + m2)v

• Initial KE:

• Final KE:

6.4 Elastic and Inelastic Collisions

The fraction of the total kinetic energy that is left after a completely inelastic collision can be shown to be:

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6.4 Elastic and Inelastic Collisions• A 1.0 kg ball with a speed of 4.5 m/s strikes a 2.0 kg stationary ball. If the collision is completely Inelastic then what are the speeds of the balls after the collision?

• What percentage of the initial kinetic energy do balls have after the collision?

• What is the total momentum after the collision?

6.4 Elastic and Inelastic Collisions

For an elastic collision, both the momentum and the kinetic energy are conserved:

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6.4 Elastic and Inelastic Collisions• Few types of elastic collisions:

• One object is initially at rest

• In this example, one of the initial velocities would be what??

• If the masses are the same, then momentum and KE are completely exchanged.

• Two colliding objects, both initially moving.

6.4 Elastic and Inelastic Collisions• To find the final velocities of both

masses in an elastic collision we have to use the following formulas:

6.4 Elastic and Inelastic Collisions• A 0.30 kg ball with a speed of 2.0 m/s in

the positive x direction has a head-on elastic collision with a stationary 0.70 kg ball.

• What are the velocities of the balls after the collision?

6.4 Elastic and Inelastic Collisions

Collisions may take place with the two objects approaching each other, or with one overtaking the other.

You are given the precollision data for 2 different elastic collisions. What are the final velocities in a? What are the final velocities in b?

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6.4 Elastic and Inelastic Collisions• Two balls of equal mass with equal but

opposite velocities approach each other for a head-on collision. After the collision the balls will: (1) move off stuck together, (2) both be at rest, (3) move off in the same direction, (4) recoil in opposite directions

• Which is the right answer. 1? 2? 3? 4?

6.5 Center of MassDefinition of the center of mass:The center of mass is the point at which all of the mass of an object or system may be considered to be concentrated, for the purposes of linear or translational motion only.Center of mass represents the whole system as a single particle, or a point mass. Another name would be the BALANCE POINT Exs: balancing a meterstick on your finger

We can then use Newton’s second law for the motion of the center of mass:

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6.5 Center of Mass• If the net external force on a system is

zero, then the total linear momentum of the center of mass is conserved.

• If net force is zero, then the center of mass is either at?? Or moving at a ??

• You already know this formula...

6.5 Center of MassThe location of the center of mass can be found:

This calculation is straightforward for a system of point particles, but for an extended object calculus is necessary.

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6.5 Center of Mass• Three masses, 2.0 kg, 3.0 kg, 6.0 kg, are

located at positions (3.0, 0), (6.0, 0), (-4.0, 0) respectively in meters from the origin. Where is the center of mass located?

• Easiest to draw a picture of what this would look like.

6.5 Center of Mass• A dumbbell has a connecting bar of

negligible mass. Find the location of the center of mass when

• Mass1 and mass2 are each 5.0 kg.

• Mass1 is 5.0 kg and mass2 is 10.0 kg. • See pic Mrs. Dubya puts on board.

6.5 Center of Mass• Mass and weight are related...much as

center of mass and center of gravity are related.

• The center of gravity is the point where all of the weight of an object may be considered to be concentrated.

• Equation?

6.5 Center of MassThe center of mass of a flat object can be found by suspension.

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6.5 Center of Mass

The center of mass may be located outside a solid object.

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Summary of Chapter 6Momentum of a point particle is defined as its mass multiplied by its velocity.The momentum of a system of particles is the vector sum of the momenta of its components.Newton’s second law:

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Summary of Chapter 6

Impulse–momentum theorem:

In the absence of external forces, momentum is conserved.Momentum is conserved during a collision.Kinetic energy is also conserved in an elastic collision.

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Summary of Chapter 6

The center of mass of an object is the point where all the mass may be considered to be concentrated. Coordinates of the center of mass:

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