Momentum is a Momentum vectors Impulse Defined as a Impulse is.
02 Impulse & Momentum
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Transcript of 02 Impulse & Momentum
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MOMENTUM(MOMENTUM(
p
p))
%f a particle is mo#ing oliquel! and has #elocit! components v&,
v!, v', then its momentum components would e:
x x mv p = y y mv p = z z mv p =
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dt pd F
=
IMPULSE(IMPULSE(
J J) - MOMENTUM() - MOMENTUM(
p
p) THEOREM) THEOREM
v1 = 0v2 > 0
∫
∑
=
2
(
2
(
p
p
t
t pd dt F
⇒
∫
∑
dt F
t 1 t 2
∑
F F ∑
F
p p pdt F
t
t
∫ ∑
(2
2
(
The change in momentum is
affected ! the applied net forceand how long it is applied
⇒
%mpulse ( J ), whose
direction is the same
as the net force.
p J ⇒
Impulse – Momentum
Theorem
The change in momentum of a particle during a time inter#al
equals the impulse of the net
force that acts on the particle
during that inter#al
⇒
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IMPULSE(IMPULSE(
J J) - MOMENTUM() - MOMENTUM(
p
p) THEOREM) THEOREM
%n specific prolems, it is often easiest to use %mpulse*Momentum
Theorem in its component form:
x x p J
x x
t
t x p pdt F
(2
2
(
∫
∑
x x
t
t x mvmvdt F (2
2
(
∫ ∑
y y p J
y y
t
t y p pdt F
(2
2
(
∫
∑
y y
t
t ymvmvdt F (2
2
(
∫ ∑
z z p J
z z
t
t z p pdt F (22
(
∫ ∑
z z
t
t z mvmvdt F
(2
2
(
∫
∑
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IMPULSE(IMPULSE(
J J) - MOMENTUM() - MOMENTUM(
p
p) THEOREM) THEOREM
+uppose !ou ha#e a choice etween catching a .-*g all
mo#ing at /. m0s or a .*g all mo#ing at 2 m0s. 1hich will
e easier to catch
Example 1.
$ .3*g hoce! puc is mo#ing on an ic!, frictionless,
hori'ontal surface. $t t 4 the puc is mo#ing to the right at 5.
m0s. a) 6alculate the #elocit! of the puc(magnitude and
direction) after a force of 2-. N directed to the right has een
applied for .- s. ) %f instead, a force of 2 N directed to theleft is applied from t 4 s to t 2 4 .- s, what is the final
#elocit! of the puc
Example 2.
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CONSERVATION OF MOMENTUMCONSERVATION OF MOMENTUM
Before Collision
Durin Collision
m! mB
! B
!fter Collision
v! vB
m!
u!
mB
uB
F !B F B!
BA AB F F " # t
t F t F BA AB
BA AB J J
= B p A p
=
(2 B B p p (2 A A p p
22(( B A B A p p p p
The total momentum of a s$stem is
%onser&e'(
B B A A B B A A umumvmvm
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CONSERVATION OF MOMENTUMCONSERVATION OF MOMENTUM
Before Collision Durin Collision !fter Collision
Bx B Ax A Bx B Ax A vmvmumum
By B Ay A By B Ay A vmvmumum
Bz B Az A Bz B Az A vmvmumum
v!$
v!x
v!$
v!x
u!x
u!$
uB$
uBx
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COLLISIONCOLLISION
Elasti% Collision ) the total inetic energ! of the s!stem efore
and after the collision is constant.
2222
2
(
2
(
2
(
2
(
B B A A B B A A umumvmvm
22(( B A B A K K K K
2222
2
(
2
(
2
(
2
( B B B B A A A A vmumumvm
2222
B B B A A A vumuvm
( .eqnvuvumuvuvm B B B B B A A A A A
⇒
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COLLISIONCOLLISION
6onser#ation of Momentum
B B B B A A A A vmumumvm
2 .eqnvumuvm B B B A A A ⇒
B B A A B B A A umumvmvm
B B B
B B B B B
A A A
A A A A A
vum
vuvum
uvm
uvuvm
=
B B A A vuuv
A B B A uuvv
eqn. 7 eqn. 2
B A B A uuvv
⇒
B A vv
⇒ B A uu
Relati#e #elocit! of approach
Relati#e #elocit! of separation
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COLLISIONCOLLISION
+o, 6oefficient of Restitution, e for 8lastic 6ollision:
(
=
B A
B Avv
uue
*ummar$+
Elasti% Collision
9 K 4 K 29 e 4
Inelasti% Collision
9 K ; K 29 e <
Completel$
Inelasti% Collision
9 K ; K 29 e 4
9 u$ 4 u=
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COLLISIONCOLLISION
$ -*gm ullet is fired from a /*g gun. The mu''le speed is 3m0s. >ind the speed of recoil of the gun.
Example ,.
$ *gm loc mo#ing with a speed of cm0s to the right
collides with a 2*g loc mo#ing with a speed of - cm0s at thesame direction. a) >ind the speed of the two locs right after the
collision if the collision is inelastic with coefficient of restitution,
e 4 .?-. ) >ind the change in inetic energ! of the s!stem.
Example -.
$ hoce! puc B rests on a smooth ice surface and is struc ! a
second puc A, which was originall! tra#elling at / m0s and
which is deflected 5o from its original direction. @uc B
acquires a #elocit! at a /-o angle to the original direction of A.
The pucs ha#e the same mass. 6ompute the speed of each puc
after the collision.
Example .
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