Theme Music: Kenny Rogers Every time two fools … · Physics 131 10/21/16 Prof. E. F. Redish 1...
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Physics 131 10/21/16 Prof. E. F. Redish 1 10/21/16 1 Physics 131 ■ Theme Music: Kenny Rogers Every time two fools collide ■ Cartoon: Bill Waterson Calvin & Hobbes October 21, 2016 Physics 131 Prof. E. F. Redish Momentum Conservation 10/21/16 Physics 131 3 ! p A i + ! p B i = ! p A f + ! p B f Δ ! p A = −Δ ! p B
Transcript of Theme Music: Kenny Rogers Every time two fools … · Physics 131 10/21/16 Prof. E. F. Redish 1...
Physics 131 10/21/16
Prof. E. F. Redish 1
10/21/16 1 Physics 131
■ Theme Music: Kenny Rogers Every time two fools collide
■ Cartoon: Bill Waterson Calvin & Hobbes
October 21, 2016 Physics 131 Prof. E. F. Redish
Momentum Conservation
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!pAi + !pB
i = !pAf + !pB
f
Δ!pA = −Δ!pB
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10/21/16 4 Physics 131
Foothold ideas: Momentum
■ We define the momentum of an object, A:
■ This is a way of defining “the amount of motion” an object has.
■ Our “delta” form of N2 becomes which we can rewrite as
pA = mA
vA
FAnet = mA
ΔvAΔt
= mAaA
FAnet =
Δ mAvA( )
Δt= ΔpA
Δt
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Foothold idea: The Impulse-Momentum Theorem ■ Newton 2
■ Put in definition of a
■ Multiply up by Δt
■ Define Impulse
■ Combine to get Impulse-Momentum Theorem for any object A
I Anet =
FAnetΔt
ΔpA =
I A
net
aA =FAnet
mA
dvAdt
=FAnet
mA
mAΔvA =
FAnetΔt
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Foothold idea: Momentum Conservation: 1
■ If two objects, A and B, interact with each other and with other (“external”) objects, By the IMθ
■ Adding: tFFvm
tFFvm
BAextBBB
ABextAAA
Δ+=Δ
Δ+=Δ
→
→
)(
)(
mA ΔvA +mB Δ
vB =FAext +FBext +
FA→B +
FB→A( )⎡⎣ ⎤⎦Δt
Δ mAvA +mB
vB( ) = FABextΔt
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Foothold idea: Momentum Conservation: 2
■ So: If two objects interact with each other in such a way that the external forces on the pair cancel, then their momentum is conserved.
( )fBB
fAA
iBB
iAA
BBAA
vmvmvmvmvmvm
+=+
=+Δ 0
⇒
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Example: Recoil ■ When an object at rest emits a part of itself,
in order to conserve momentum, it must go back in the opposite direction.
■ What forces are responsible for this motion?
(object goes backwards)
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