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Unformatted text preview: = = mi i dm
Fnet,ext = M mi i
a
i Momentum............. i
=a m v
Fnet,ext
Deﬁne total momentum : = P mi i ii
Deﬁne total momentum :P = i mii
v
i
i
dP
Deﬁne total momentum : dPP =
mi i
v
Then : Fnet,ext =
Then : Fnet,ext dt
=
i
dt
dP
Then
F
T ∝ : L/g net,ext =
dt
T ∝ L/g
π = 3.141592653589793....
π = 3.141592653589793.... Applications of Momentum:
Impulse: how much momentum does a force impart if it acts
over a small time interval?
Collisions with no external forces. We’ll see, momentum is
conserved.
Rocket propulsion: momentum conservation in a continuous
fashion.
Fnet,ext = mi i
a Impulse
i A useful concept when an external forcects on an object over a
a=
Deﬁne total momentum :
P
mi i
v
short time interval Δt. Example: bat hitting a baseball. Refer to
i
the external force as Fimp .
dP for the change of
From Fext = d p/dt , we
have a simple formula
Then : Fnet,ext =
dt
momentum Δp:
Fimp ∆t = ∆p
Impulsive Forces: strong deformations in
short time intervals. Impulse video Ex. A tennis ball (m = 0.060 kg) strikes a
tennis racket with velocity 30 m/s (→) and
rebounds with velocity 40 m/s (←) in the
opposite direction.
(a) What are the magnitude and direction of
the ball's change in momentum ? DEMO (1/A) 0.60 kgm/s →
(2/B) 0.60 kgm/s ←
(3/C) 4.2 kgm/s →
(4/D) 4.2 kgm/s ←
(5/E) Other v
p Look here !! v
p f o +x: → v
Δp Δp = p
x fx − p ox = m v fx − m v ox = (0.060 kg)( 40 m/s  30 m/s) ( = m v fx − v ox ) =  4.2 kgm/s v
Δp = 4.2 kgm / s ← (b) If the ball is in contact with the racket for 6 ms (= 0.006 s), what is the
average impact force on the ball due to the racket during this time?
impulsive force — acts for only a
“brief” time Δt
average force
during impact (Δt): v
F avg = v
Δp
Δt Same area as
under actual F
(t) vs. t graph F(t) Favg
t 0 v
F avg = 4.2 kgm / s ←
0.006 s = 700 N ← Impact
time Δt...
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This note was uploaded on 09/29/2012 for the course MATH 1920 taught by Professor Pantano during the Spring '06 term at Cornell University (Engineering School).
 Spring '06
 PANTANO
 Multivariable Calculus

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