Chapter 9: Momentum Chapter 9: Momentum and Conservationand Conservation

Newton’s Laws appliedNewton’s Laws applied

Dynamics of PhysicsDynamics of Physics

Dynamics are the CAUSES of Dynamics are the CAUSES of CHANGE in Physics.CHANGE in Physics.

Recall that position is changed by Recall that position is changed by velocity.velocity.

Velocity is changed by acceleration.Velocity is changed by acceleration. Acceleration is caused by a net force.Acceleration is caused by a net force. Properties that remain constant are Properties that remain constant are

described as CONSERVED.described as CONSERVED.

Impulse and MomentumImpulse and Momentum Momentum is described by Newton’s 3 Momentum is described by Newton’s 3

laws of motion as the laws of motion as the quantity of quantity of motionmotion..

If no net force acts on a body, its If no net force acts on a body, its velocity is constant.velocity is constant.

If a net force acts on a body, velocity If a net force acts on a body, velocity is changed. (acceleration)is changed. (acceleration)

Forces on objects change over time. Forces on objects change over time. Identify “before”, “during”, and “after” Identify “before”, “during”, and “after”

in an interaction.in an interaction.

Developing Impulse Developing Impulse

F = ma can be rewritten to substitute a rate of F = ma can be rewritten to substitute a rate of change in velocity for acceleration.change in velocity for acceleration.

multiplying both sides by multiplying both sides by ΔΔt, then t, then

ImpulseImpulse is a force over a period of time. (N*s) is a force over a period of time. (N*s) Since a FORCE causes a velocity to CHANGE, Since a FORCE causes a velocity to CHANGE,

then an then an IMPULSEIMPULSE causes causes MOMENTUMMOMENTUM to to change. (kg*m/s)change. (kg*m/s)

t

vmF

vmtF

Impulse-Momentum TheoremImpulse-Momentum Theorem

12 vvv 12 mvmv Can also be stated as

The symbol for Momentum is ρ. Thus, ρ= mv.

Impulse = Change in Momentum

The force is not constant, and the impulse is found using the AVERAGE FORCE times the time interval, or finding the area under the curve of a force-time graph.

12 tF

VectorsVectors Velocity is a vector, so momentum is Velocity is a vector, so momentum is

a vector.a vector. Force is a vector, so impulse is a Force is a vector, so impulse is a

vector.vector. Vectors have positive and negative Vectors have positive and negative

directions associated with them. directions associated with them. Traditionally, positive direction is Traditionally, positive direction is right and left is negative.right and left is negative.

Saving lives with PhysicsSaving lives with Physics A large change in momentum comes A large change in momentum comes

from a large impulse.from a large impulse. Since Impulse is FSince Impulse is FΔΔt, you can have a t, you can have a

large force OR a large time of contact large force OR a large time of contact to produce a large impulse. to produce a large impulse.

In a car crash, an air bag extends the In a car crash, an air bag extends the TIME of contact to reduce the FORCE TIME of contact to reduce the FORCE of impact. The Impulse is the same of impact. The Impulse is the same whether you hit the air bag, or the whether you hit the air bag, or the steering wheel. Thus the steering wheel. Thus the ΔΔmv is the mv is the same.same.

Car crash video clip Car crash with seatbelts

Angular MomentumAngular MomentumJust like linear momentum is mv, a Just like linear momentum is mv, a

ROTATING object has momentum ROTATING object has momentum also. The momentum of a rotating also. The momentum of a rotating object is called object is called Angular MomentumAngular Momentum and depends on the object’s mass, and depends on the object’s mass, distance from the center axis of distance from the center axis of rotation, and tangential velocity. If rotation, and tangential velocity. If the radius gets smaller, the velocity the radius gets smaller, the velocity increases to maintain constant increases to maintain constant angular momentum. Like water angular momentum. Like water going down the toilet, or a hurricane, going down the toilet, or a hurricane, or planets around a star (sun).or planets around a star (sun).

Practice ProblemPractice ProblemA 0.144kg baseball is pitched A 0.144kg baseball is pitched

horizontally at 38.0m/s. After it is hit horizontally at 38.0m/s. After it is hit by the bat, it moves at the same by the bat, it moves at the same speed, but in an opposite direction. speed, but in an opposite direction.

What was the change in momentum What was the change in momentum of the ball?of the ball?

What was the impulse delivered by What was the impulse delivered by the bat? the bat?

Batter Up SolutionBatter Up Solution

Given: mGiven: mballball =0.144kg, v=38.0 m/s, =0.144kg, v=38.0 m/s, +direction = direction after ball leaves +direction = direction after ball leaves batbat

Unknown: FUnknown: FΔΔt = t = ΔρΔρSolve:Solve:

ΔρΔρ= mv= mv22-mv-mv11 =m(v =m(v22 – v – v11)) = (0.144kg)(38.0m/s-(-38.0m/s))= (0.144kg)(38.0m/s-(-38.0m/s)) = (0.144kg)(76.0m/s) = 10.9 kg-m/s= (0.144kg)(76.0m/s) = 10.9 kg-m/sImpulse = change in momentum Impulse = change in momentum = 10.9 N-s= 10.9 N-s

Your turn to practiceYour turn to practiceDo pg. 204-205 Practice Problems # Do pg. 204-205 Practice Problems #

1,2,3,4,5,61,2,3,4,5,6

Do pg.217 #s 1,2,4,6,7Do pg.217 #s 1,2,4,6,7

Do pg. 218 #s 22-27Do pg. 218 #s 22-27

Conservation of MomentumConservation of Momentum

Forces are a result of an interaction between Forces are a result of an interaction between objects moving in opposite directions. objects moving in opposite directions.

During collisions, the force of one object on During collisions, the force of one object on another is = in strength but opposite in another is = in strength but opposite in direction to the force of the second object on direction to the force of the second object on the first. the first.

The time interval for the force is the same for The time interval for the force is the same for both objects, so the Impulse is = and opposite.both objects, so the Impulse is = and opposite.

AonBBonA FF

What about Momenta?What about Momenta?

According to the I-M theorem, the final According to the I-M theorem, the final momentum = the impulse + the initial momentum = the impulse + the initial momentum.momentum.

In a collision, the final momenta must be In a collision, the final momenta must be equal to the sum of the initial momenta in a equal to the sum of the initial momenta in a system and thus Momentum is Conserved. system and thus Momentum is Conserved.

12 tF

1122 BABA

Defining Closed SystemsDefining Closed Systems A system that doesn’t gain or lose A system that doesn’t gain or lose

mass is said to be a mass is said to be a closed systemclosed system.. All forces within a closed system are All forces within a closed system are

called called internal forcesinternal forces.. All forces outside a closed system are All forces outside a closed system are

considered considered external forcesexternal forces.. In a system, objects that collide can In a system, objects that collide can

either stick together (inelastic either stick together (inelastic collision), or come apart (elastic collision), or come apart (elastic collision). Momentum of the collision collision). Momentum of the collision in a closed system with no net in a closed system with no net external force is still conserved.external force is still conserved.

Car collision problemCar collision problem

A 2275kg car going 28m/s rear-ends an 875kg A 2275kg car going 28m/s rear-ends an 875kg compact car going 16m/s on ice in the same compact car going 16m/s on ice in the same direction. The cars stick together. How fast direction. The cars stick together. How fast does the wreckage move after the collision?does the wreckage move after the collision?

Car crash solutionCar crash solution1122 BABA

BA

BBAA

mm

vmvmv

112

Because the cars stick together, their velocities after the collision are equal. So, vA2 = vB2 = v2

mAvA1 + mBvB1 = (mA+mB)v2

So v2 = 25 m/s, as we can see when mass increases, velocity must decrease to conserve momentum.

)8752275(

)/16)(875()/28)(2275(2 kgkg

smkgsmkgv

ExplosionsExplosions As with the 2 skaters in Fig 9-8, if they both As with the 2 skaters in Fig 9-8, if they both

start at rest and A gives B a push, both start at rest and A gives B a push, both skaters will move in opposite directions. skaters will move in opposite directions. The push is an internal force. The total The push is an internal force. The total momentum of the system must be zero momentum of the system must be zero after the push as it was zero before the after the push as it was zero before the push. The momenta of the skaters will be push. The momenta of the skaters will be equal and opposite after the push. equal and opposite after the push.

The chemicals in a rocket exploding to The chemicals in a rocket exploding to propel the rocket are internal forces as they propel the rocket are internal forces as they are expelled into space propelling the are expelled into space propelling the rocket along.rocket along.

mmAAvvA2A2 = -m = -mBBvvB2B2

Ch 9 HomeworkCh 9 Homework

Please complete the following:Please complete the following: Pg. 210 Prac. Probs. # 7,8,9, &12Pg. 210 Prac. Probs. # 7,8,9, &12 Pg. 218 Rev #s 28,34,35, and 36.Pg. 218 Rev #s 28,34,35, and 36.