MOMENTUM MOMENTUM AND COLLISIONSAND COLLISIONS

Momentum is the product of Momentum is the product of the mass and velocity of a the mass and velocity of a body. Momentum is a vector body. Momentum is a vector quantity that has the same quantity that has the same direction as the velocity of direction as the velocity of the object. the object.

MOMENTUMMOMENTUM

MOMENTUMMOMENTUM

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PROBLEM 1PROBLEM 1

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A 2250 kg pickup truck has a velocity A 2250 kg pickup truck has a velocity of 25 m/s to the east. What is the of 25 m/s to the east. What is the momentum of the truck?momentum of the truck?

Impulse is the product of the Impulse is the product of the average force and the time average force and the time interval during which the force interval during which the force is exerted.is exerted.

IMPULSE-MOMENTUM IMPULSE-MOMENTUM THEOREMTHEOREM

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Applications of Impulse Momentum Applications of Impulse Momentum TheoremTheorem

Used to determine stopping distances Used to determine stopping distances and safe following distances of cars and and safe following distances of cars and trucks.trucks.

Used in designing safety equipment that Used in designing safety equipment that reduces force exerted on the object reduces force exerted on the object during collisions. Example-nets and giant during collisions. Example-nets and giant air mattresses for fire-fighters.air mattresses for fire-fighters.

Also used in sports equipment and Also used in sports equipment and games.games.

A baseball of mass 0.14 kg is moving at 35 m/s. A) Find the momentum of the baseball.

B) Find the velocity of a bowling ball, mass 7.26 kg, if its momentum is the same as the baseball.

PROBLEM 3PROBLEM 3

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The brakes exert a 640 N force on a car weighing 15689 N and moving at 20 m/s. The car finally stops. A) What is the car’s mass? B) What is the car’s initial momentum? C) What is the change in the car’s momentum?D) How long does the braking force act on the car to bring it to a halt?

PROBLEM 6PROBLEM 6

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CONSERVATION OF CONSERVATION OF MOMENTUMMOMENTUM

States that the momentum of any closed, isolated system does not change.

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Isolated System has no net force acting on it.Closed System is a system in which objects neither enter nor leave .

Glider A of mass .355 kg moves along a frictionless air track with a velocity of .095 m/s. It collides with a glider B of mass .710kg moving in the same direction at a speed of .045m/s. After collision glider A continues in the same direction with a velocity of .035 m/s. What is the velocity of glider B after collision?

PROBLEM 11PROBLEM 11

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Internal forces are forces between objects within a system.

Example: If we consider a single car as our system, forces are exerted on objects within the car during a collision (i.e. a crash dummy)

INTERNAL FORCESINTERNAL FORCES

External force is a force exerted by an object outside the system.

Example: if car A was our system, and it collides with car B. Then the force car B exerts on car A is an external force.

EXTERNAL FORCESEXTERNAL FORCES

Two campers dock a canoe. One camper steps on the dock. This camper has a mass of 80 kg and moves forward at 4 m/s. With what speed and direction do the canoe and the other camper move if their combined mass is 110 kg?

PROBLEM 17PROBLEM 17

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Types of CollisionsTypes of Collisions

ELASTIC – objects are apart ELASTIC – objects are apart after the collisionafter the collision

INELASTIC – objects “stick” INELASTIC – objects “stick” together after the collisiontogether after the collision

COLLISIONSCOLLISIONS

INELASTICINELASTICMomentum is Momentum is

conservedconservedSome kinetic Some kinetic

energy is energy is changed into changed into other formsother forms

ELASTICELASTICMomentum is Momentum is

conserved.conserved.Energy is Energy is

conserved.conserved.

ELASTIC COLLISIONSELASTIC COLLISIONS

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INELASTIC COLLISIONSINELASTIC COLLISIONS

A 15-kg medicine ball is thrown at a velocity of 20 km/hr to a 60-kg person who is at rest on ice. The person catches the ball and subsequently slides with the ball across the ice. Determine the velocity of the person and the ball after the collision. Such a motion can be considered as a collision between a person and a medicine ball. Before the collision, the ball has momentum and the person does not. The collision causes the ball to lose momentum and the person to gain momentum. After the collision, the ball and the person travel with the same velocity ("v") across the ice.

Before Before Collision Collision

After After Collision Collision

Person Person 0 0 60 * v 60 * v

Medicine ball Medicine ball 300 300 15 * v 15 * v

Total Total 300 300 300 300

km/hr 4 v

300 75v

300 15v 60v

Before Collision Before Collision After Collision After Collision

Granny Granny 80 * 6 = 480 80 * 6 = 480 80 * v 80 * v

Ambrose Ambrose 0 0 40 * v 40 * v

Total Total 480 480 480 480

4m/s v

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Before Collision Before Collision After Collision After Collision

Truck Truck 3000 * 10 = 30 000 3000 * 10 = 30 000 3000 * v 3000 * v

Car Car 0 0 1000 * 15 = 15 000 1000 * 15 = 15 000

Total Total 30 000 30 000 30 000 30 000

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Elastic

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Elastic

Above is a representation of  3 bullets with equal mass running into 3 blocks of wood with equal mass. The first bullet passes through the block and maintains much of its original momentum   As a result, very little momentum gets transferred to the block. The second bullet, expands as it enters the block of wood which prevents it from passing all the way through it.  As a result, most of its momentum gets transferred to the block.  (This is a totally inelastic collision.) The third bullet (a rubber bullet) bounces off the block transferring all of it's own momentum and then borrowing some more from the block.  This has the most momentum transferred to the block.  (This is an elastic collision.)

KE and Collisions

Elastic KE is conserved: no sound or heat produced

sub atomic particles, repelling magnets, a“perfect” super ball

Inelastic (partially elastic) some KE is lost as heat or sound

Is a broad range containing most collisions

Completely Inelastic more KE is lost as heat or sound the colliding objects stick together

PROBLEM 20PROBLEM 20

A 2575 kg van runs into the A 2575 kg van runs into the back of a 825kg compact back of a 825kg compact car at rest. They move off car at rest. They move off together at 8.5 m/s. together at 8.5 m/s. Assuming no friction with Assuming no friction with the ground, find the initial the ground, find the initial speed of the van.speed of the van.

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PROBLEM 21PROBLEM 21

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