lec 18 ( impulse & momentum 042)
TRANSCRIPT
-
8/9/2019 LEC 18 ( Impulse & Momentum 042)
1/16
King Fahd University ofPetroleum & Minerals
Mechanical EngineeringDynamics ME 201
B
Dr! Meyassar "! #l$%addadecture ' 1(
-
8/9/2019 LEC 18 ( Impulse & Momentum 042)
2/16
-
8/9/2019 LEC 18 ( Impulse & Momentum 042)
3/16
== mmaF
=2
1
2
1
vF
t
t
v
vdmdt
Principle of linear impulse and momentum e"uation
=2
1
12 vvF
t
t
mmdt
change in momentumImpulse
#e$ton%s &econd 'a$
dt
dv
-
8/9/2019 LEC 18 ( Impulse & Momentum 042)
4/16
'inear momentum
' ( mv Measure of impact effect
Compare
bullets with small mass and high velocity
Ship with huge mass and slow velocity
L is a vector )) points in same direction as v
*nit: +g.m,s or slug.ft,s
-omponents rectangular coordinates/: '0(mv0 '!(mv! '1(mv1
-
8/9/2019 LEC 18 ( Impulse & Momentum 042)
5/16
'inear Impulse
Measure the effect of force during the time
force acts.
I is a vector "uantit! in the direction of force
*nit #.s or Ib.s
2hen 3 is constant
=2
1
F(t)It
t
dt
)(FI 12 ttc =
-
8/9/2019 LEC 18 ( Impulse & Momentum 042)
6/16
Principle of 'inear Impulse and
Momentum
=+2
1
21 vFv
t
t
mdtm
Initial momentum 4 &um of all Impulse ( 3inal momentum
{ } 21 mtNtNtmgtFm cc =++++
-
8/9/2019 LEC 18 ( Impulse & Momentum 042)
7/16
Principle of 'inear Impulse and Momentum
for a s!stem of Particles
=+2
1
21 )(vF)(v
t
t
iiiiimdtm
=+2
1
2G1G )v(F)v(t
t
mdtm
== iiGi mmmm vv
-
8/9/2019 LEC 18 ( Impulse & Momentum 042)
8/16
&calar 5"uations
=+2
1
21 )()(
t
t
xxx mdtFm
=+2
1
21 )()(
t
t
yyy mdtFm
=+2
1
21 )()(
t
t
zzz mdtFm
-
8/9/2019 LEC 18 ( Impulse & Momentum 042)
9/16
3ree 6od! 7iagram
&elect the particle
5stablish 0 ! frame
5stablish the direction of theparticle initial and finalvelocities
7re$ the impulseand momentdiagrams. Include all theforces acting on the particle%s367 $ill create an impulseeven though some of these
forces $ill do no $or+. 8esolving the vectors along
the 0 ! a0is
9ppl! =+
2
1
2xx1x )(F)(
t
t
mdtm
=+2
1
2yy1y )(F)(
t
tmdtm
-
8/9/2019 LEC 18 ( Impulse & Momentum 042)
10/16
50ample ;)
m((?
#(?
=++ 2
1
21 )()()(
t
t
xxx mdtFm
sm
kgsN o
/1.14
)100()10(45cos2000
2
2
=
=+
( ) =++
2
1
21 )()(
t
tyyy
mdtFm
NN
sNsNsN
c
o
c
840
045sin)10(200)10(981)10(0
=
=++
=0yF
-
8/9/2019 LEC 18 ( Impulse & Momentum 042)
11/16
50ample ;)@
2(;< Ib
P(>(?T(> sec.
=(@ ft,s
+(
-
8/9/2019 LEC 18 ( Impulse & Momentum 042)
12/16
50ample ;)@
3rom rest
v6(?
t(A sec.
=++2
1
21 )()()(
t
t
AyA mdtFm
6loc+ 9
2))(3()6)(81.9(3)6(20 AkgssT =+
6loc+ 6
=++2
1
21 )()()(
t
t
ByB mdtFm
2))(5()6()6)(81.9(50 BkgsTs =+
BA
BA lSS
=
=+
2
2
NT
sm
B
B
2.19
/8.35)( 2
=
=
-
8/9/2019 LEC 18 ( Impulse & Momentum 042)
13/16
Problem ;)B
m(> Mg
3!(;< +#
=(?
h(?t(A s
&tart from rest
( ) =++2
1
21 )()(
t
t
yyy mdtFm
sm /1.16
)10(12)6)(81.9)(10(12)6)(10(1500
2
2
333
=
=+
( )
2
0
/69.2
)6(01.16
sma
a
tavv c
=
+=+=+
( )
ms
s
tatvssc
4.48
)6)(69.2(2
100
2
1
2
2
00
=
++=
++=+
-
8/9/2019 LEC 18 ( Impulse & Momentum 042)
14/16
Problem ;)A
m ( >C Mg
9t rest
=( ?t ( B s
3 ( B )
-
8/9/2019 LEC 18 ( Impulse & Momentum 042)
15/16
Problem ;)D
m ( E; +g
&tart from rest
v ( >
-
8/9/2019 LEC 18 ( Impulse & Momentum 042)
16/16