conservation-of-momentum-ppp-1213361160074257-8 (1)

8/12/2019 conservation-of-momentum-ppp-1213361160074257-8 (1)

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The Law of Conservation ofMomentum


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The Law of Action-Reaction A collision is an interaction between two

objects which have made contact

(usually) with each other. A collision results in a force being

applied to the two colliding objects.

Such collisions are governed byNewton's laws of motion.


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Newton's third law of motion

In every interaction, there is a pair of forcesacting on the two interacting objects.

The size of the force on the first object equalsthe size of the force on the second object.

The direction of the force on the first object isopposite to the direction of the force on the

second object.Forces always come in pairs - equal andopposite action-reaction force pairs.


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Newton's third law of motionapplied to collisions between

two objects.In a collision between two objects, both objects

experience forces which are equal in

magnitude and opposite in direction.Such forces cause one object to speed up (gain

momentum) and the other object to slowdown (lose momentum).

According to Newton's third law, the forces onthe two objects are equal in magnitude.


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Effect of collisions on

accelerationWhile the forces are equal in magnitude

and opposite in direction, the

acceleration of the objects are notnecessarily equal in magnitude.


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And so, in comes Newtons

Second Law of MotionThe acceleration of an object is

dependent upon both force and mass.

Thus, if the colliding objects have unequalmass, they will have unequalaccelerations as a result of the contact

force which results during the collision.


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Example: A collision occursbetween the moving club head

and the stationary golf ball.


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You can observe unequal

accelerations.Although there is a high speed given to

the ball as the result of the collision, you

are not observing unequal forces uponthe ball and club head.


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F = m * a

Since club head and ball experienceequal forces, but the mass of the ball is

much smaller than that of the club,acceleration will be bigger.

The least massive object receives the

greatest acceleration.


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Collisions between equal-

mass objects

Each objectexperiences thesame acceleration.


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While driving down the road,Anna observed a bug striking

the windshield of her car.

Which of the two forces is greater: the force on

the bug or the force on the windshield?Trick question! They are equal.

Which has the greater acceleration: bug orwindshield?

The bug and because of its smaller mass, it is

unable to withstand this large acceleration.


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Rockets are unable to

accelerate in space because...a) there is no air in space for the rockets

to push off of.

b) there is no gravity is in space.

c) there is no air resistance in space.

d) ...nonsense! Rockets do accelerate inspace.


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gun reco s w en s re .The acceleration of the

recoiling gun is ...a) greater than the acceleration of the bullet.

b) smaller than the acceleration of the bullet.

c) the same size as the acceleration of thebullet.

(The recoil is the result of action-reaction force pairs. As the gases from the gunpowderexplosion expand, the gunpushes the bulletforwards and the bulletpushes the gunbackwards.)


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Airplane Wing Design

Why is it important that an airplane wingbe designed so that it deflects oncoming

air downward?


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Jumping to the Dock

Would it be a good idea to jump from arowboat to a dock that seems within

jumping distance? Explain.


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You throw a ball horizontallywhile standing on roller

skates.What Happens?

You roll backward with a momentum that

matches that of the ball.

Will we roll backward if we go through themotion of throwing the ball withoutletting go of it? Explain.


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Momentum ConservationPrinciplehttp://www.glenbrook.k12.il.us/gbssci/phys/Class/momentum/u4l2b.html
http://www.glenbrook.k12.il.us/gbssci/phys/Class/momentum/u4l2b.htmlhttp://www.glenbrook.k12.il.us/gbssci/phys/Class/momentum/u4l2b.htmlhttp://www.glenbrook.k12.il.us/gbssci/phys/Class/momentum/u4l2b.htmlhttp://www.glenbrook.k12.il.us/gbssci/phys/Class/momentum/u4l2b.html


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the law of conservation of

momentumFor a collision occurring between object 1

and object 2 in an isolated system, the

total momentum of the two objectsbefore the collision is equal to the totalmomentum of the two objects after the

collision.


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the law of conservation of

momentum the momentum lost by object 1 is equal

to the momentum gained by object 2

total momentum of a collection ofobjects (a system) is conserved

the total amount of momentum is a

constant or unchanging value.


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A short, logical proof:

Consider a collision between two objects -object 1 and object 2. For such a collision, the

forces acting between the two objects areequal in magnitude and opposite in direction.This statement can be expressed in equationform as follows:

F1= -F2


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The forces act between thetwo objects for a given amount

of time.Regardless of how long the time is, it can be

said that the time that the force acts uponobject 1 is equal to the time that the forceacts upon object 2.

This is merely logical; forces result frominteractions (or touching) between twoobjects.

As an equation, this can be stated as

t1= t2


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e mpu sesexper ence ythe two objects are also equal

in magnitude and opposite indirectionThis follows from the facts that

a. the forces between the two objects areequal in magnitude and opposite indirection, and

b. the times for which these forces act are

equal in magnitude, it follows that As anequation, this can be stated as

F1 t1 = -F2 t2


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The impulse given to theobject is equal to the change

in momentum of that object

Thus, since each object experiences equal andopposite impulses, it follows logically that theymust also experience equal and oppositemomentum changes. As an equation, this canbe stated as

m1 v1= -m2v2


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1 v1= - 2

v2The above equation is one statement ofthe law of momentum conservation.

In a collision, the momentum change ofobject 1 is equal and opposite to themomentum change of object 2.

That is, the momentum lost by object 1 isequal to the momentum gained byobject 2.

e o a momen m o e


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e o a momen um o esystem(the collection of two

objects) is conserved.In a collision between two objects, one object

slows down and loses momentum while the

other object speeds up and gains momentum.If object 1 loses 75 units of momentum, then

object 2 gains 75 units of momentum.

Notice that the total momentum of the two

objects (object 1 plus object 2) is the samebefore the collision as it is after the collision.

co s on s g m s es


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co s on s g m s, es(review the section on adding

vectorsif necessary).Therefore, the total

momentum of the system afterthe collision must also be 20kg*m/s, West. The fullback

and the linebacker movetogether as a single unit after

the collision with a combined*

o e sys em e ore e
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o e sys em e ore ecollision is 80 kg*m/s.

Therefore, the totalmomentum of the system afterthe collision must also be 80kg*m/s. The clown and the

medicine ball move together

as a single unit after thecollision with a combined

momentum of 80 kg*m/s. ana ys s se u means o


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ana ys s. se u means orepresenting such analyses

include a momentum tableand a vector diagram. Later in

Lesson 2, we will use themomentum conservation

principle to solve problems in

which the after-collisionvelocity of objects is predicted.


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high-speed water.


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c. Which vehicle experiencesthe greatest momentum

change?d. Which vehicle experiences

the greatest acceleration?

was no no cea e c ange n


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was no no cea e c ange nthe speed of the bus

compared to the obviouschange in the speed of the

bug. Ben disagrees entirely,arguing that that both bug andbus encounter the same force,

momentum change, andimpulse. Who do you agree

with? Support your answer.


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____________feel this? Explain.

s e reco ve oc y o e


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s e reco ve oc y o eEarth (mass = 6.0 x 10^24

kg).

w c e e ore an a er


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w c e e ore- an a er-collision momenta of each

player is represented by amomentum vector. Label the

magnitude of each momentumvector.

See answer below.


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Answer to Question #6

Return to question #6.

e prev ous par o esson
http://www.glenbrook.k12.il.us/gbssci/phys/Class/momentum/u4l2b.htmlhttp://www.glenbrook.k12.il.us/gbssci/phys/Class/momentum/u4l2b.html


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e prev ous par o essonfocused on the Law of

Conservation of Momentum. Itwas stated that ...

i d b bj
http://www.glenbrook.k12.il.us/gbssci/phys/Class/momentum/u4l2b.htmlhttp://www.glenbrook.k12.il.us/gbssci/phys/Class/momentum/u4l2b.html


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momentum gained by object2.

Total system momentum isconserved for collisions

occurring in isolated systems.But what makes a system ofobjects an isolated system?

And is momentum conservedif the system is not isolated?

This is the focus of this part of orce ere are wo cr er a


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orce. ere are wo cr er afor the presence of a net

external force; it must be...a force which originates froma source other than the two

objects of the systema force that is not balanced by

other forces.

th t b ll th


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upon the two balls are thecontact forces which they

apply to one another. Thesetwo forces are considered

internal forces since theyresult from a source within thesystem - that source being the

contact of the two balls. Forsuch a collision, total system

momentum is conserved t l f


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external force.CollisionDescriptionIsolated System?Yes or NoIf No, then theexternal force is...


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Two cars collide on a gravelroadway on which frictionalforces are large.


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vacuuming. Hans is pushingthe Hoover vacuum cleaneracross the living room carpet.

i th t ld b


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money in the system would be$200 both before and after the

transaction; total systemmoney would be conserved. If

however, a third influenceenters from outside of the

system to take away or (morefortunately) to add money tothe system, then total system

momentum would not be


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aw ecomes a power u aw nphysics because it allows forpredictions of the before- andafter-collision velocities (ormass) of an object. In thisportion of Lesson 2, the law ofmomentum conservation will

be used to make suchpredictions. The law of


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medicine ball. Before thecollision, the ball hasmomentum and the persondoes not. The collision causesthe ball to lose momentumand the person to gainmomentum. After the collision,the ball and the person travelwith the same velocity ( v )


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60 * v

Medicine ball300

15 * vTotal


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both the objects after thecollision), set the sum of theindividual momentum of thetwo objects equal to the totalmomentum. The followingequation results:60*v + 15*v = 30075*v = 300v = 4 km/hr


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e ve oc y o ranny anAmbrose. Assume that noexternal forces act on thesystem so that it is an isolatedsystem.Before the collision, Grannyhas momentum and Ambrose

does not. The collision causesGranny to lose momentum


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After CollisionGranny80 * 6 = 480

80 * vAmbrose0


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problem for v (the velocity ofboth persons after thecollision), set the sum of theindividual momentum of thetwo objects equal to the totalmomentum. The followingequation results:80*v + 40*v = 480120*v = 480


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mec an ca orms o energysuch as heat energy andsound energy. The subject ofenergywill be treated in alater unit of The PhysicsClassroom. To simplifymatters, we will consider any

collisions in which the twocolliding objects stick together
http://www.glenbrook.k12.il.us/gbssci/phys/Class/energy/energtoc.htmlhttp://www.glenbrook.k12.il.us/gbssci/phys/Class/BBoard.htmlhttp://www.glenbrook.k12.il.us/gbssci/phys/Class/BBoard.htmlhttp://www.glenbrook.k12.il.us/gbssci/phys/Class/BBoard.htmlhttp://www.glenbrook.k12.il.us/gbssci/phys/Class/BBoard.htmlhttp://www.glenbrook.k12.il.us/gbssci/phys/Class/energy/energtoc.html


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two objects will bounce offeach other. While this is nottechnically an elastic collision,it is more elastic than

collisions in which the twoobjects stick together.


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ruc a er e co s on.In this collision, the truck hasa considerable amount ofmomentum before thecollision and the car has nomomentum (it is at rest). Afterthe collision, the truck slows

down (loses momentum) andthe car speeds up (gainsmomentum).


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3000 * vCar0

1000 * 15 = 15 000Total30 000


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momentum of the truck (v isthe velocity of the truck afterthe collision). To solve theproblem for v (the velocity of

the truck), set the sum of theindividual after-collisionmomentum of the two objectsequal to the total momentum.The following equation results:


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a ema ca represen a onsare just one of the manyrepresentations of physicsconcepts. Avoid merelytreating these collisionproblems as meremathematical exercises. Takethe time to understand theconcept of momentumconservation which provides


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There are similar practiceproblems (with accompanyingsolutions)lower on this pagewhich are worth the practice.

However, let's first take amore cognitive approach tosome collision problems. Thequestions which follow providea re ltest of your conceptual


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4 km/hr (with respect to theship) bumps into you. If sheholds onto you, how fast doyou move (with respect to the

ship)?


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e sma er an e e orecollision velocity. How manytimes smaller must it be? Bywhat factor must the velocitybe decreased? Before thecollision, the amount of massin motion is m; after thecollision, the amount of massin motion is 2*m. The amountof mass in motion has doubled


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another variable. The constantquantity in a collision is themomentum (momentum isconserved). For a constant

momentum value, mass andvelocity are inverselyproportional. Thus, anincrease in mass results in adecrease in velocity.


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ou a s orm o pro em-solving is limited to situationsin which one of the twoobjects is at rest before thecollision and both objectsmove at the same speed afterthe collision. To further test

your understanding of thistype of quantitative reasoning,try the following two


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e mass o e sma er s ,then what is the speed of thelarge fish (and the smallerfish) after the collision?Depress mouse on pop-upmenu to view answer.
http://www.glenbrook.k12.il.us/gbssci/phys/mmedia/momentum/fca.html


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a - g goa e a res .


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what velocity does the goalieslide on the ice after catchingthe puck?


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The block and bullet movetogether at 8.6 m/s. What wasthe original velocity of thebullet? (CAUTION: Be carefulof the units on velocity.)

eav ng a m s. e oc


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was at rest when it was hit.How fast is it moving when thebullet leaves? (CAUTION: Becareful of the units onvelocity.)

oppos e rec on a a ve oc y


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of -12.0 m/s. The 0.50-kg ballmoves away at -14 m/s afterthe collision. Find the velocityof the second ball.


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and move with the samevelocity after the collision.Determine the post-collisionvelocity of the car and truck.

(CAREFUL: Be cautious of the+/- sign on the velocity of thetwo vehicles.)

e same ve oc y a er e


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collision. Determine the thepost-collision velocity of thetwo players. (CAREFUL: Becautious of the +/- sign on thevelocity of the two players.)

http://www.glenbrook.k12.il.us/


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Astronaut Catch

Imagine that you are hovering next to the

space shuttle in earth-orbit and your

buddy of equal mass who is moving 4 m/s(with respect to the ship) bumps into you.

If she holds onto you, then how fast do

the two of you move after the collision?


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A question like this involves

momentum principles.In any instance in which two objects collide and

can be considered isolated from all other netforces, the conservation of momentum

principle can be utilized to determine the post-collision velocities of the two objects. Collisionsbetween objects are governed by laws ofmomentum and energy. When a collision

occurs in an isolated system, the totalmomentum of the system of objects isconserved. Provided that there are no netexternal forces acting upon the two astronauts,

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