Impulse and Momentum

Impulse = MomentumConsider Newtons 2nd Law and the definition of acceleration

Units of Impulse: Units of Momentum:Momentum is defined as Inertia in MotionNsKg x m/s

Impulse Momentum TheoremIMPULSECHANGE IN MOMENTUMThis theorem reveals some interesting relationships such as the INVERSE relationship between FORCE and TIME

Impulse Momentum Relationships

Impulse Momentum RelationshipsConstantSince TIME is directly related to the VELOCITY when the force and mass are constant, the LONGER the cannonball is in the barrel the greater the velocity.

Also, you could say that the force acts over a larger displacement, thus there is more WORK. The work done on the cannonball turns into kinetic energy.

How about a collision?Consider 2 objects speeding toward each other. When they collide......

Due to Newtons 3rd Law the FORCE they exert on each other are EQUAL and OPPOSITE.

The TIMES of impact are also equal.

Therefore, the IMPULSES of the 2 objects colliding are also EQUAL

How about a collision?If the Impulses are equal then the MOMENTUMS are also equal!

Momentum is conserved!The Law of Conservation of Momentum: In the absence of an external force (gravity, friction), the total momentum before the collision is equal to the total momentum after the collision.

Types of Collisions A situation where the objects DO NOT STICK is one type of collisionNotice that in EACH case, you have TWO objects BEFORE and AFTER the collision.

ANo Stick type collisionSpbefore =Spafter-10 m/s

Types of CollisionsAnother type of collision is one where the objects STICK together. Notice you have TWO objects before the collision and ONE object after the collision.

AStick type of collisionSpbefore =Spafter 5 m/s

The explosion typeThis type is often referred to as backwards inelastic. Notice you have ONE object ( we treat this as a SYSTEM) before the explosion and TWO objects after the explosion.

Backwards Inelastic - ExplosionsSuppose we have a 4-kg rifle loaded with a 0.010 kg bullet. When the rifle is fired the bullet exits the barrel with a velocity of 300 m/s. How fast does the gun RECOIL backwards?Spbefore =Spafter-0.75 m/s

Collision SummarySometimes objects stick together or blow apart. In this case, momentum is ALWAYS conserved.When 2 objects collide and DONT stickWhen 2 objects collide and stick togetherWhen 1 object breaks into 2 objectsElastic Collision = Kinetic Energy is ConservedInelastic Collision = Kinetic Energy is NOT Conserved

Elastic CollisionSince KINETIC ENERGY is conserved during the collision we call this an ELASTIC COLLISION.

Inelastic CollisionSince KINETIC ENERGY was NOT conserved during the collision we call this an INELASTIC COLLISION.

ExampleGranny (m=80 kg) whizzes around the rink with a velocity of 6 m/s. She suddenly collides with Ambrose (m=40 kg) who is at rest directly in her path. Rather than knock him over, she picks him up and continues in motion without "braking." Determine the velocity of Granny and Ambrose.How many objects do I have before the collision?

How many objects do I have after the collision?214 m/s

Collisions in 2 DimensionsThe figure to the left shows a collision between two pucks on an air hockey table. Puck A has a mass of 0.025-kg and is moving along the x-axis with a velocity of +5.5 m/s. It makes a collision with puck B, which has a mass of 0.050-kg and is initially at rest. The collision is NOT head on. After the collision, the two pucks fly apart with angles shown in the drawing. Calculate the speeds of the pucks after the collision.vAvBvAcosqvAsinqvBcosqvBsinq

Collisions in 2 dimensionsvAvBvAcosqvAsinqvBcosqvBsinq

Collisions in 2 dimensions

The Question

Change in momentum: Dp = pafter - pbeforeTeddy Bear: Dp = 0-(-mv) = mv Bouncing Ball: Dp = mv-(-mv) = 2mvChange in Momentum ACTIf the bear and the ball have equal masses, which toy experiences the greater change in momentum?

Change in Momentum ACT2 A 10 kg cart collides with a wall and changes its direction. What is its change in x-momentum Dpx? -30 kg m/s -10 kg m/s 10 kg m/s 20 kg m/s 30 kg m/s

Pushing Off Fred (75 kg) and Jane (50 kg) are at rest on skates facing each other. Jane then pushes Fred w/ a constant force F = 45 N for a time Dt=3 seconds. Who will be moving fastest at the end of the push?A) FredB) SameC) JaneFredF = +45 N (positive direct.)I = +45 (3) N-s = 135 N-sI = Dp = mvf mvi I/m = vf - vivf = 135 N-s / 75 kg = 1.8 m/sJaneF = -45 N Newtons 3rd lawI = -45 (3) N-s = -135 N-sI = Dp = mvf mvi I/m = vf - vivf = -135 N-s / 50 kg = -2.7 m/sNote: Pfred + Pjane = (1.8) 75 + (-2.7) 50 = 0!

You drop an egg onto 1) the floor 2) a thick piece of foam rubber. In both cases, the egg does not bounce. In which case is the impulse greater?A) FloorB) FoamC) the same In which case is the average force greaterA) Floor B) FoamC) the sameI = DPSame change in momentum same impulseDp = F DtF = Dp/DtSmaller Dt = larger FACTs

Momentum Change ACTA car w/ mass 1200 kg is driving north at 40 m/s, and turns east driving 30 m/s. What is the magnitude of the cars change in momentum?A) 0B) 12,000 C) 36,000D) 48,000E) 60,000Pinitial = m vinitial = (1200 Kg) x 40 m/s = 48,000 kg m/s NorthPfinal = m vfinal = (1200 Kg) x 30 m/s = 36,000 kg m/s EastNorth-South:Pfinal Pinitial = (0 48000) = -48,000 kg m/sEast-West:Pfinal Pinitial = (36000 - 0) = +36,000 kg m/sMagnitude :Sqrt(P2North P2East ) = 60,000 kg m/s40 m/s30 m/s

Thank You For AttentionSee You Next Time. . .

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