Chapter 8: Momentum - Concordia University...
Transcript of Chapter 8: Momentum - Concordia University...
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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
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! p = m
! v
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! 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.
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! F avΔt = Δ
! p
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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
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! 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:
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v1 =m1 − m2
m1 + m2
#
$ % %
&
' ( ( v
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v2 =2m1
m1 + m2
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# $ $
%
& ' ' 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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