Chapter 8: Momentum - Concordia University...

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1 Chapter 8: Momentum Brent Royuk Phys-111 Concordia University Linear Momentum • Definition: • Units • Multiple Objects – Take the vector sum to get the total for the system • Newton’s Second Law ! p = m ! v ! F = m ! a = m ! v ! v o ( ) Δt = Δ ! p Δt 2 Impulse • Rearrange the previous equation: – Units – Impulse = F Δt only if F is constant. • Otherwise you have to find the area under the curve of a F-t graph. ! F av Δt = Δ ! p 3

Transcript of Chapter 8: Momentum - Concordia University...

Page 1: Chapter 8: Momentum - Concordia University Nebraskaestrada.cune.edu/facweb/brent.royuk/phys111/docs/Chapter08_3.pdfConservation of Momentum • Examples – A 75 kg man is riding on

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Chapter 8: Momentum

Brent Royuk Phys-111

Concordia University

Linear Momentum • Definition: • Units • Multiple Objects

– Take the vector sum to get the total for the system

• Newton’s Second Law

! p = m

! v

! F ∑ = m

! a =

m! v −

! v o( )

Δt=Δ! p Δt

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Impulse • Rearrange the previous equation:

– Units –  Impulse = F Δt only if F is constant.

• Otherwise you have to find the area under the curve of a F-t graph.

! F avΔt = Δ

! p

3

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Impulse Examples •  Push a 50 kg box with a force of 200 N

for 3.0 s. How fast is it going? •  A 0.10 kg golf ball gets teed off at 40

m/s in 1.0 ms. How hard was it hit?

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The Impulse Bargain

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The Impulse Bargain •  Bend legs when landing. •  Let glove recoil when

catching a baseball. •  Follow through when

batting to increase contact time.

•  Airbags

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Conservation of Momentum •  So we have •  What if Fnet = 0? •  The Law

–  If the net force acting on an object is zero, its momentum is conserved.

•  Internal vs. External Forces

! F ∑ =

Δ! p Δt

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Conservation of Momentum

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Conservation of Momentum •  Before and after pictures •  “Professor Goddard does not know the relation

between action and reaction and the need to have something better than a vacuum against which to react. He seems to lack the basic knowledge ladled out daily in high schools.” 1921 New York Times editorial about Robert Goddard's revolutionary rocket work. "Correction: It is now definitely established that a rocket can function in a vacuum. The Times regrets the error." NY times, July 1969.

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Conservation of Momentum •  Examples

– Two skaters stand facing each other and push against each other’s hands. Their masses are 80 kg and 60 kg. If the 80 kg skater moves away at a speed of 1.2 m/s, how fast is the other skater moving? •  Springy-dingy go-karts

– A stream of bullets, each with a mass of 3.8 g, is fired horizontally with a speed of 1100 m/s into a large wooden block of mass 12 kg at rest on a frictionless table. How fast will the block be moving if it absorbs 8 bullets?

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Conservation of Momentum •  Examples

– A 75 kg man is riding on a 39 kg cart traveling at a speed of 2.3 m/s. He jumps off in such a way as to land on the ground with zero horizontal speed. What is the new speed of the cart?

– A motionless 50 kg boy on ice skates catches a 2.0 kg medicine ball and subsequently moves with a speed of 2.0 m/s. How fast was the ball moving? Is this realistic?

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Collisions • Example

– Consider two 2000 kg boxcars. One moves at 1.0 m/s and hits the other, coupling. Find speed with momentum. Compare kinetic energies.

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Elastic vs. Inelastic •  Momentum is always conserved, energy

need not be. •  Elastic = bouncy? yes

– Things that stick together are completely inelastic: clay vs. superballs.

– Happy/unhappy balls •  Derive fractional energy relationship for

completely inelastic collisions (stationary target) – Little hitting big vs. big hitting little – Go-Carts

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Elastic vs. Inelastic

• Consider: Final velocities in a completely elastic collision with a stationary target

• Result:

v1 =m1 − m2

m1 + m2

#

$ % %

&

' ( ( v

v2 =2m1

m1 + m2

"

# $ $

%

& ' ' v

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Elastic Collisions

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Newton’s Cradle

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2-D Collisions

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2-D Collisions •  A collision occurs as described below. Both

balls have the same mass. Find the speeds of both balls after the collision. –  The Billiard Ball Law

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The Ballistic Pendulum

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