Chapter 18 Section 3Chapter 18 Section 3

CollisionsCollisions

MassMass

Mass is the amount of matter in an objectMass is the amount of matter in an object

The mass of an object affects how easy it The mass of an object affects how easy it is to changes its motion.is to changes its motion.

InertiaInertia

Inertia is the tendency of an object to Inertia is the tendency of an object to resist a change in its motion.resist a change in its motion.

The amount of resistance to a change in The amount of resistance to a change in its motion increases as an objectits motion increases as an object’’s mass s mass increases.increases.

MomentumMomentum

The momentum of an object is a measure The momentum of an object is a measure of how hard it is to stop the object.of how hard it is to stop the object.

Increasing the speed or velocity of an Increasing the speed or velocity of an object makes it harder to stop.object makes it harder to stop.

Momentum has direction that is the same Momentum has direction that is the same as the direction of the velocity.as the direction of the velocity.

Momentum EquationMomentum Equation

Momentum( kg x m/s) = mass (kg) x velocity (m/s)Momentum( kg x m/s) = mass (kg) x velocity (m/s)

p=momentum m=mass v=velocityp=momentum m=mass v=velocity

P

M V

Solve the Equation 1Solve the Equation 1

Calculate the momentum of a 14kg bicycle Calculate the momentum of a 14kg bicycle traveling north at 2 m/s.traveling north at 2 m/s.

Answer 1Answer 1

(14kg) (2 m/s north) = 28 kg·m/s north(14kg) (2 m/s north) = 28 kg·m/s north

Solve the Equation 2Solve the Equation 2

A 10,000 kg train is traveling east at A 10,000 kg train is traveling east at

15 m/s. Calculate the momentum of the 15 m/s. Calculate the momentum of the train.train.

Answer 2Answer 2

10,000 kg x 15 m/s east = 150,000 kg·m/s east10,000 kg x 15 m/s east = 150,000 kg·m/s east

Solve the Equation 3Solve the Equation 3

What is the momentum of a car with a What is the momentum of a car with a mass of 900 kg traveling north at 27 m/s?mass of 900 kg traveling north at 27 m/s?

Answer 3Answer 3

900 kg x 27 m/s north = 24,300 kg · m/s north900 kg x 27 m/s north = 24,300 kg · m/s north

The Law of Conservation of The Law of Conservation of MomentumMomentum

In any collision, momentum is transferred In any collision, momentum is transferred from one object to another.from one object to another.

The momentum lost by one object is equal The momentum lost by one object is equal to the momentum gained by the other to the momentum gained by the other object.object.

The law states that the total momentum of The law states that the total momentum of a group of objects remains constant a group of objects remains constant unless outside forces act on the group.unless outside forces act on the group.

Example of the LawExample of the Law

In a game of billiards (pool), when the cue In a game of billiards (pool), when the cue ball hits the other billiard balls, it slows ball hits the other billiard balls, it slows down because it transfers some of its down because it transfers some of its momentum to the other billiard balls.momentum to the other billiard balls.

What would happen to the speed of the What would happen to the speed of the cue ball if all its momentum were cue ball if all its momentum were transferred to the other billiard balls?transferred to the other billiard balls?

An Example of an Outside ForceAn Example of an Outside Force

An outside force, An outside force, like frictionlike friction, can change , can change the total momentum of the group of the total momentum of the group of objects.objects.

Types of CollisionsTypes of Collisions

Bounce off of each other, like bowling ball Bounce off of each other, like bowling ball and pins (elastic)and pins (elastic)

Collide and stick to each other, like one Collide and stick to each other, like one football player tackles another. (inelastic)football player tackles another. (inelastic)

Example of Momentum Example of Momentum ConservationConservation

Suppose two balls approach each other at Suppose two balls approach each other at 1 m/s from opposite directions. Their total 1 m/s from opposite directions. Their total momentum is zero. After collision, they momentum is zero. After collision, they both zoom off at 1 m/s in opposite both zoom off at 1 m/s in opposite directions. What is their momentum? What directions. What is their momentum? What do you know about the mass of the two do you know about the mass of the two balls?balls?

AnswerAnswer

If the total momentum is zero and the two If the total momentum is zero and the two balls have the same speed in the opposite balls have the same speed in the opposite direction, the balls must have the same direction, the balls must have the same mass.mass.

PredictionsPredictions

Then law of momentum conservation can Then law of momentum conservation can be used to predict the velocity of objects be used to predict the velocity of objects after they collide.after they collide.

Suppose a 2 kg backpack initially has a Suppose a 2 kg backpack initially has a velocity 5 m/s east. Your mass is 48 kg, velocity 5 m/s east. Your mass is 48 kg, and initially youand initially you’’re at rest then the total re at rest then the total initial momentum is-initial momentum is-

2 kg x 5 m/s + 48 kg x 0 m/s = 10 kg · m/s 2 kg x 5 m/s + 48 kg x 0 m/s = 10 kg · m/s easteast

P= mvP= mv

You can now use the equation for You can now use the equation for momentum to find the final velocity.momentum to find the final velocity.

10 kg · m/s/east = 2 kg + 48 kg x velocity10 kg · m/s/east = 2 kg + 48 kg x velocity

10 kg · m/s/east = 50 kg x velocity10 kg · m/s/east = 50 kg x velocity

0.2 m/s east = velocity0.2 m/s east = velocity

The ending velocity is smaller (0.2 m/s east) The ending velocity is smaller (0.2 m/s east) is smaller than the initial velocity (5 m/s is smaller than the initial velocity (5 m/s east) east)

Visualize what will happen.Visualize what will happen.

If small car is stopped at a red light is hit If small car is stopped at a red light is hit from behind by a truck, what will happen?from behind by a truck, what will happen?

AnswerAnswer

Both vehicles will move forward with the Both vehicles will move forward with the car moving faster than the truck.car moving faster than the truck.

Visualize what will happen.Visualize what will happen.

What will happen if two marbles of the What will happen if two marbles of the same mass, traveling towards each other, same mass, traveling towards each other, collide?collide?

AnswerAnswer

The marbles will collide and reverse The marbles will collide and reverse direction, moving away from each other at direction, moving away from each other at the same speed as before the collision.the same speed as before the collision.

ConclusionConclusion

Momentum equals the mass of an object Momentum equals the mass of an object times its velocitytimes its velocity

Momentum is transferred from one object Momentum is transferred from one object to another in a collision.to another in a collision.

The total amount of momentum of a group The total amount of momentum of a group does not change unless acted upon by an does not change unless acted upon by an outside force/s.outside force/s.