Impulse and Momentum

1
Impulse and Momentum

• (Two Dimensions)

2
Impulse

• Impulse is a vector
• IFtI, ?
• IxFxt IyFyt
• Ix(Fcos?)t Iy(Fsin?)t

I(Ix)x(Iy)y
3
Multiple Impulses
I1
I1I1, ?1 I2I2, ?2
I2
ITxI1cos?1I2cos?2 ITyI1sin?1I2sin?2 IT(IT
x)x(ITy)y
4
Momentum

• Momentum is a vector
• pp, ? pmv v speed
• px(pcos?) py(psin?)

p(px)x(py)y
Momentum of a system
5
Momentum in a System
p1p1, ?1 p2p2, ?2
p1
p2
pTxp1cos?1p2cos?2 pTyp2sin?1p2sin?2 pT(pT
x)x(pTy)y
6
Change in Momentum
p1p1, ?1 p2p2, ?2

• ?pp2-p1
• ?pxp2x-p1xp2cos ?2-p1cos ?1
• ?pyp2y-p1yp2sin ?2-p1sin ? 1
• ?p(?px)x(?py)y

?p?p, ?
7
The Impulse-Momentum Theorem(graphic)
F
p2
p1
FF, ? p1p1,?1 p2p2, ?2
8
Impulse Momentum
IxFxtp2x-p1x IyFytp2y-p2y (Fcos?)tp2cos
?2-p1cos ?1 (Fsin?)tp2sin ?2-p1sin ?1
9
A Two Dimensional Collision
p1
p2
p1
p2
10
Conservation of MomentumTwo Object
Elastic/Inelastic Collision
p p x p1cos?1p2cos?2p1cos?1p2cos?2
y p1sin?1p2sin?2p1sin?1p2sin?2
11
Conservation of MomentumTwo Object Perfectly
inelastic Collision
p p x p1cos?1p2cos?2(m1m2)v1,2cos?1,2
y p1sin?1p2sin?2(m1m2)v1,2sin?1,2