Momentur _
and Energy-
Linear Momentum : The product of the mass and velocity of an object
4 = m .
v
---------------------
! Always choose negative and positive direction
P · Momentum
(kg .
m .
s") ! for objects Momentum- ---------
"
m mass
(kg)
va velocity (m st) .
st
Charge In Momentum-
5 m .
-
If mass is constant (2(g) st
5m
-
.
&P = Pf- Pi
(7 5) (5)]
-
= MDV 0x = 2 - -
~
= m(Vt Vi) -
=
- 20
=
-
20kg .
m
.
"West
s
-Rate ot Change amomentum
The net force object equal to the rate of
acting on an is
change momentum
-P ------
Y
Fret = 47
Fret
The net force object
·
on experiences in a collision
-Conservation_ etLinear Momentum _
Pet = Paft
Objects move separately :
1
--------------------
- -
Vi Both
M
, + MaVzi =
MiVif + MaVas ! objects
change in momentum " experience equal
·
! NetForceand contact time is equal FretO=
Before After
-
4m st 15 m
. st
st
.
2 m .
?
60kg zokg 60kg zokg
Pi = Xf
M .Ki + MaVzi =
MiVif + MaVaf
(60)(4) + (20)) 2) -
= (60)(1 5) . + (20)V25
V2f = 5 5 .
m
.
s" East
, Objects Stick
together :
Becomes one object
-
M .Vi + mzVi = (M , + M2) Vf
Before After
5 m .
s Im st
?
.
V =
3kg 7kg 3kg 7 kg
Pi = Pf
M Vi
. + maVai = (mitma)Vt
(3)(5) + (7)) 1) - = (20)Vf
Vf s
Right
: = 0 8 m
.
,
-Elastic _
and _
Enelastic Collisions
Elastic Collision : Collision in which both momentum and kinetic
energy are conserved
Inelastic Collision : Collision in which
only momentum is conserved
El = mu
Before After
12 m S .
- I
Om s 6m .
s =?
.
V
2kg 6kg 2kg 6kg
M
, Vi + MaVzi =
MiVif + MaVas Elinitial = miv + mava Elfinal = mvi" + EmaV,
>
(2)((2) + (6) (0) =
(2)) 6) -
+ 6Vf = E (2)(x2) =(b) (0)
+ 2(2) ( 6) =(6)(6)"
=
+
VF 6 m s"
= .
right = 144] = 1445
: Collision is elastic
-Erpulse-
The product of the netforce and the contact time
Fret Ot = J - - - - - - - - - - - - - - -
imIi
Enet
Or
Ot = Op
I
I
will increase momentum
is constant then
change of
increasing time
i
---------------------
Fret ↑
net force (N)
* * collision time (S)
- 5
change momentum
a
in impulse
Finding exerted force:
Enet =
OX
= m(Vz- Vi)
8t
and Energy-
Linear Momentum : The product of the mass and velocity of an object
4 = m .
v
---------------------
! Always choose negative and positive direction
P · Momentum
(kg .
m .
s") ! for objects Momentum- ---------
"
m mass
(kg)
va velocity (m st) .
st
Charge In Momentum-
5 m .
-
If mass is constant (2(g) st
5m
-
.
&P = Pf- Pi
(7 5) (5)]
-
= MDV 0x = 2 - -
~
= m(Vt Vi) -
=
- 20
=
-
20kg .
m
.
"West
s
-Rate ot Change amomentum
The net force object equal to the rate of
acting on an is
change momentum
-P ------
Y
Fret = 47
Fret
The net force object
·
on experiences in a collision
-Conservation_ etLinear Momentum _
Pet = Paft
Objects move separately :
1
--------------------
- -
Vi Both
M
, + MaVzi =
MiVif + MaVas ! objects
change in momentum " experience equal
·
! NetForceand contact time is equal FretO=
Before After
-
4m st 15 m
. st
st
.
2 m .
?
60kg zokg 60kg zokg
Pi = Xf
M .Ki + MaVzi =
MiVif + MaVaf
(60)(4) + (20)) 2) -
= (60)(1 5) . + (20)V25
V2f = 5 5 .
m
.
s" East
, Objects Stick
together :
Becomes one object
-
M .Vi + mzVi = (M , + M2) Vf
Before After
5 m .
s Im st
?
.
V =
3kg 7kg 3kg 7 kg
Pi = Pf
M Vi
. + maVai = (mitma)Vt
(3)(5) + (7)) 1) - = (20)Vf
Vf s
Right
: = 0 8 m
.
,
-Elastic _
and _
Enelastic Collisions
Elastic Collision : Collision in which both momentum and kinetic
energy are conserved
Inelastic Collision : Collision in which
only momentum is conserved
El = mu
Before After
12 m S .
- I
Om s 6m .
s =?
.
V
2kg 6kg 2kg 6kg
M
, Vi + MaVzi =
MiVif + MaVas Elinitial = miv + mava Elfinal = mvi" + EmaV,
>
(2)((2) + (6) (0) =
(2)) 6) -
+ 6Vf = E (2)(x2) =(b) (0)
+ 2(2) ( 6) =(6)(6)"
=
+
VF 6 m s"
= .
right = 144] = 1445
: Collision is elastic
-Erpulse-
The product of the netforce and the contact time
Fret Ot = J - - - - - - - - - - - - - - -
imIi
Enet
Or
Ot = Op
I
I
will increase momentum
is constant then
change of
increasing time
i
---------------------
Fret ↑
net force (N)
* * collision time (S)
- 5
change momentum
a
in impulse
Finding exerted force:
Enet =
OX
= m(Vz- Vi)
8t
