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STATICS & DYNAMICS
!"#$%& FINAL
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!"!"#$ MECHANICS FINAL EXAM
1 MOTION OF PARTICLE VELOCITY AND ACCELERATION
Velocity
Acceleration
with Constant Acceleration
RECTANGULAR COORDINATE(x-y)
v =ds
dt =
!s
a =dv
dt = !v
ads =vdv
v = v 0 +at
s = s 0 +v
0 t +
1
2at
2
v 2= v
2
0 + 2a (s ! s 0 )
!r = x
+ y
!v =
!"r = v
x
+v y j
!a =
!""r = a
x
+ ay j
v x =
v y =
ax =
ay =
v = !
v =
a =
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!"!"#$ MECHANICS FINAL EXAM
Motion of Projectile!"#$%"&'()*+,-.// projectile
Horizontal :
Vertical :
ax = ay =
v x = v
x ( )
0
x = x 0 + v
x ( )0 t
v y = v y ( )0!gt
v 2
y = v
y ( )2
0! 2g (y ! y 0)
y = y 0 + v y ( )0 t ! 1
2gt 2
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y
x
a g
(v0) y
(v0) x
v0
v x
v yv
r
y0
y
x0
x
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!"!"#$ MECHANICS FINAL EXAM
1. 012&343,()5+67+8&"9!6)&:6;, 869&(") )
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!"!"#$ MECHANICS FINAL EXAM
2. O"P,B+6"&'Q6R0SCD:6-GA A T6UI 869&V1K+6(W,0&3>&K+6O"P,-1+6GA A M/.,
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!"!"#$ MECHANICS FINAL EXAM
NORMAL AND TANGENTIAL COORDINATE (n-t)
.", tangential (t) ]+
.", normal (n) ]+
,
Note: 1. (^+_>`()*+,-(a,(W,>'6
2. (^+_>`()*+,-4b6J
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!"!"#$ MECHANICS FINAL EXAM
3. [final 2554] I:+"()*+,-8&" A c6 B>&1'&64b6 /,'%,&/ de[ 16 m J
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!"!"#$ MECHANICS FINAL EXAM
POLAR COORDINATE (r-#) Velocity
4A3-
Acceleration
4A3-
Note: 1. "&'()*+,-(a,
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!"!"#$ MECHANICS FINAL EXAM
4. [final 2556] +mn&) P ()*+,-HIA&1(W,f&6(o,UIp,9+3>&1UI 4A3- R=4+0.25t 2 m .:% ! =2 " t rad (^+ t ]+(
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!"!"#$ MECHANICS FINAL EXAM
5. s,HA'ET/(gt6u"++".//1&CDvA++"J
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!"!"#$ MECHANICS FINAL EXAM
RELATIVE MOTION (Translation Axes)
4A3-
4A3-
6. (z+4{f0+6|++"8&"L&C,(&1kef&6T6UI }& v A = 20 m/s .:% vB = 15 m/s 86~,
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!"!"#$ MECHANICS FINAL EXAM
7. C,Y&,€.•696 (z+'/ A :&A>'%(
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!"!"#$ MECHANICS FINAL EXAM
2 FORCE AND ACCELERATION FRICTION
EQUATION OF MOTION
F = µ
N
P
mg
Pm
! = m
P
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!"!"#$ MECHANICS FINAL EXAM
8. [final 2556] 01969O" 60 kg Ž+"Z+6 9 kg v,+‡C,t-[)":6;,869&.'6 R .:% L *
R = 846 N, L = 110.4 N ; R,L$0
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Problem 3/4
9 kg
60 kg
g––4
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!"!"#$ MECHANICS FINAL EXAM
9. "Z+6!69O" 50 kg 86~,
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!"!"#$ MECHANICS FINAL EXAM
MOTION OF CONNECTED PARTICLES
CURVILINEAR MOTION
!F n = ma
n
!F t =ma
t
an =
at =
!F r =ma
r
!F " =ma
"
a r =
a ! =
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an
O¿
P
at
a
O
r
ar
au
a
u
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!"!"#$ MECHANICS FINAL EXAM
10. .'6 P = 40 N "'%‘-"Z+6 B T6UI -(”1B,"Z+6 A .:% B 9A–6M/- 869&)
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!"!"#$ MECHANICS FINAL EXAM
9. [final 2/2554] 'E1+(>+‹H—˜B+6™/F&1š,›,/,E,,K$%œ&, Hš&$8'&8' 4A3‰9,ACDš,›,[de[)
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!"!"#$ MECHANICS FINAL EXAM
10. .L6 ABO 9V,C,.,
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!"!"#$ MECHANICS FINAL EXAM
3 WORK AND ENERGY WORK
Definition of Work
Work of a Constant Force
Work of Friction
Note :
dU = F !ds
U 1!2
= PLcos!
P
dr
x
y
α
L
1 2
U 1!2 = PL cos! !
µ k NL
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Fc
F c cos u s2 s1
su
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!"!"#$ MECHANICS FINAL EXAM
WORK AND ENERGY EQUATION
Kinetic Energy
Potential Energy
Large Change in Altitude
No Force acting on the Particle
POWER
( )
EFFICIENCY
T 1+V
1+U
1!2 =T
2 +V
2
T =
1
2mv 2
V =V e +V g
V e =
1
2kx
2
V g =mgh
T 1 +V 1 =T 2 +V 2
P =dU
dt = F !v 1 W = 1 J/s
e =P output
P input
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V e 0
Unstretchedposition, s 0
s
s
k
k
k
V e ks21
2
V e ks21
2
V g = 0
V g = mgh
mg
h
Earth
m e
r
m
R
V g = –mgR2—–—r
mgR2—–—r2
V g = !mgR
2
r
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!"!"#$ MECHANICS FINAL EXAM
11. I:+".9
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!"!"#$ MECHANICS FINAL EXAM
12. I:+"1&1.",.,
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!"!"#$ MECHANICS FINAL EXAM
13. [final 2/2554] µ"¶11
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!"!"#$ MECHANICS FINAL EXAM
4 IMPULSE AND MOMENTUM
4A3- (º3"Š&
Note :
!F = ma = m dv
dt
!F dt t 1
t 2
" = m dv
v 1
v 2
"
mv 1+ !F dt
t 1
t 2
" =mv 2
!F dt t 1
t 2
"
mv x 1+ !F dt
t 1
t 2
! = mv x 2
mv y 1 + !F dt t 1
t 2
! = mv y 2
!F dt t 1
t 2
"
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ΣF dtt1
t2
G1 =mv1
G2 =mv2
+ =
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!"!"#$ MECHANICS FINAL EXAM
14. µ"(/0/+:1
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!"!"#$ MECHANICS FINAL EXAM
CONSERVATION OF MOMENTUM
Impact
!"#$%&'()*$+, (Coefficient of Impact)
)*$+,-.. 2 /0
!mv 1 = !mv
2
m Av A +m B v B =m A !v A +m B !v B
e =
!v B " !v
A
v A "v
B
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!"!"#$ MECHANICS FINAL EXAM
16. 'EHK,Q6Á,b& A 1
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!"!"#$ MECHANICS FINAL EXAM
17. 869&š1I'%ÁfÅ"&'2, e }&V19!62,(a,)Æ696K+6Ç+,"&'2, ! T6UI ‰9,A ! = 40° *
e = 0.434
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Problem 3/253
v v′
θ θ
––2
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!"!"#$ MECHANICS FINAL EXAM
18. f'6":11
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