When x v of the guide is 100 mm/s and is not changing at this...
Transcript of When x v of the guide is 100 mm/s and is not changing at this...
7. The pin P is forced to move in the fixed parabolic slot by the moving
vertical guide. The centerline of the slot is described by y = 0.015x2 [mm].
When x = 40 mm, the speed v of the guide is 100 mm/s and is not changing at
this instant. Determine the magnitudes N1 and N2 of the forces which the
guide and the vertical plate, respectively, exert on the 50 g pin.
mg+n
N1
N2q
+t
slotparabolicbyPonactingForceN
guideverticalbyPonactingForceN
xdx
dy
o
x
:
:
19.50
2.103.0tan
2
1
40
q
q
Kinematics:
ja
smmxxxxy
xaxvjiv
smmxxyxy
P
xxP
dt
d
300
/300)040100(03.0)(03.0
0constant120100
/120)100)(40(03.003.0015.0
22
2
Kinetics:
1
60607850
300501950819050
0
12
22
2121
N
yyy
xx
N.NN.N
...cosN..macosNmgmaF
sinNNsinNNmaF
q
mg+n
N1
N2q
+t
P
8. A 0.8-kg slider is propelled upward at A along the fixed curved bar which
lies in a vertical plane. If the slider is observed to have a speed of 4 m/s as it
passes position B, determine, (a) the magnitude N of the force exerted by the
fixed rod on the slider and (b) the rate at which the speed of the slider is
increasing. Assume that friction is negligible.
Normal&Tangential Coordinates
+ t
+ n
+ t
+ n
mg
N
man
mat
FBD KD
2905430 s/m.amasinmgmaF tttt
N
at
N.N
..cos..amcosmgNmacosmgNmaF
v
nnnn
5314
60
48030819803030
2
2
nntt maFmaFamF ,
9. The small object is placed on the inner surface of the conical dish at the
radius shown. If the coefficient of static friction between the object and the
conical surface is 0.30, for what range of angular velocities w about the
vertical axis will the block remain on the dish without slipping? Assume that
speed changes are made slowly so that any angular acceleration may be
neglected.
Normal&Tangential Coordinatesy
+ n
30o
+ n FfmsN
mg
FfmsN N
30o
(for wmax)
(for wmin)
rmNNmaF
mgNNF
snn
sy
230cos30sin
030sin30cos0
wm
m
for wmax
s/rad.sincos
cossin
r
g
rm
mg
cosNsinN
sinNcosN
rmcosNsinN
mgsinNcosN
mgsinNcosN
s
smax
s
s
s
s
s
2173030
3030
3030
3030
3030
3030
03030
2
2
m
mw
wm
m
wm
m
m
1
2
1
2
for wmin
s/rad.sincos
cossin
r
g
rm
mg
cosNsinN
sinNcosN
rmcosNsinN
mgsinNcosNmgsinNcosN
s
smin
s
s
s
ss
4133030
3030
3030
3030
3030
303003030
2
2
m
mw
wm
m
wm
mm 3
4
3
4
ms=0.30
10. The 1 kg collar slides along the smooth parabolic rod in the vertical
plane toward point O. The spring whose stiffness is k=600 N/m has an
unstretched length of 1 m. If, at the position shown in the figure, velocity of
the collar is 3.5 m/s, determine the force acting on the collar by the
parabolic rod for this instant. Neglect the friction.
m=1 kg, k=600 N/m, lo= 1 m, v=3.5 m/s, the force on the collar by the parabolic rod. Normal&Tangential Coordinates
N.Nam..cos.cosmgN
s/m..
.vmacosFcosmgNmaF
nkg
nspnn
84196873644692254469
771324853
53
1
222
mymx 5.0375.09
32375.0 2
Final length of the spring:
(Compressed)
NlkFsp 225
m.lll
m...l
o 3750
6250375050 22
o
.x
.xdx
dytan 4469
9
64
3750
m
dx
yd
dx
dy
2485.3
1
2
2
2/32
oo 87.3613.5375.0
1tan
(Radius of curvature at x=0.375 m)
+ t
+ n
q
mgFsp
N
q
1 m
11. The slotted arm revolves in the horizontal plane about the fixed vertical
axis through point O. The 2 kg slider C is drawn toward O at the constant rate of
50 mm/s by pulling the cord S. At the instant for which r=225 mm, the arm has
a counterclockwise angular velocity w=6 rad/s and is slowing down at the rate
of 2 rad/s2. For this instant, determine the tension T in the cord and the
magnitude N of the force exerted on the slider by the sides of the smooth radial
slot. Indicate which side, A or B, of the slot contacts the slider.
Polar Coordinates(Horizontal plane)+ r
T
mar
+ q
N
maq
NNNmaF
NTT
rrmTmaF
maFmaFamF
sradsradsmrmmr
rr
rr
1.2605.022225.02
2.166225.002
,
/2,/6,)constant(/05.0,225
2
2
2
q
N
(Side B)
12. The 1.2 N particle B is forced to move in the circular slot DE by the slotted arm OC.
Determine the forces P and Q exerted by the arm OC and circular slot DE on the particle B,
respectively at the instant when q =20°. Motion occurs in the horizontal plane. (b=50 cm).
At this instant, .225015 s/rad,s/rad qq
b
b
q
C
O
BD
E
225015 s/rad,s/rad qq
b
bq
O
B
Polar Coordinates(Horizontal plane)
q
r
r
Q
Rq
q
q
N.Q
...
.cosQ
maF rr
0166
1594094296819
2120 2
N.R
...
.sinQR
maF
4732
151352250940819
2120
22 942962
1352
9402
s/m.rcossinbr
s/m.rsinbr
m.rcosbr
qqqq
q
for b=50 cm=0.5 m and q=20o
q
q
rra
rrar
2
2
13. The 1.5 kg cylinder C travels along the path described by r=(0.6sinq)
[meter]. If arm OA rotates counter clockwise with a constant angular velocity of
=3 rad/s, determine the force exerted by the smooth slot in arm OA on the
cylinder at the instant q = 60°. The spring has a stiffness of 100 N/m and is
unstretched when q =30°. Motion occurs in the vertical plane.
q
m=1.5 kg r =(0.6sin q ). =3 rad/s (cst), the force exerted by the slot on the cylinder at
q = 60°. K=100 N/m , spring is unstretched when q =30°. Motion in the vertical plane.
q
03 qq )cst(s/rad
Polar Coordinates(Vertical plane)
m.sin.rsin.r 5190606060 q
22
3
6764609060 s/m.sincos.rs/m.cos.r qqqqqq
222 4523479 s/m.rras/m.rrar qqq q
Spring is unstretched when q =30°.
m.rwhen
m.rwhen
o
o
519060
3030
q
q
N..rkF
m...r
spring 9212190100
2190305190
(Spring is compressed)
222 4523479 s/m.rras/m.rrar qqq q
mg
Fspring
N
+r
+q
R
q60o30o
30o
N.N
..cosNcos...
macosNcosmgF
maF
rspring
rr
81323
347951303081951921
3030
N.R
..Rsin.sin..
maRsinNsinmg
maF
3627
1455130813233081951
3030
q
14. The 1 kg ball A, which slides in a
slot in the rotating arm OB, is kept in
contact with the stationary cam C by a
spring. The spring has a stiffness of
1000 N/m and is unstretched when
the arm OB is in position OP. If the
arm rotates with the constant angular
velocity =20 rad/s (ccw), calculate
the normal force N which the cam
exerts on A and also the force R
exerted on A by the sides of the slot
when q=30o. All surfaces are smooth.
The problem occurs in vertical plane.
r=0.1(2+cos q) m
0.2 m
0.1 m 0.3 m
q
P
C
r
y
x
B
A
Q
q
r=0.1(2+cos q) m
0.2 m
0.1 m 0.3 m
q
P
C
r
y
x
B
A
Q
+r
+q
q30o
b
b?+n
30o
q
q
q
q
e.ev
s/m..r
s/msin.r
m.cos.r
ererv
r
r
73251
7325202860
110
286030210
mg
R
N
Fspring
Kinematics
o..
arctan 997325
1
b
+r
+q
q30o
b
+n
b
+t
qv
rv
v
mg
R
N
Fspring
The spring is unstretched when the arm OB is in position OP.
r=0.1 m when the spring is unstretched.r=0.286 m when q=30o.
N..rkFspring 1861028601000
30o
30o
+r
+q
b
+n
NRR
maRNmgmaF
748.384019.9sin132.4230cos81.91
9.9sin30cos
qqq
NNN
maFNmgmaF rspringrr
132.4204.14911869.9cos30sin81.91
9.9cos30sin
2
0
22
222
0
/4020122/04.14920286.064.34
/64.3430cos201.0cossin1.0
smrrasma
smr
r
qqqq
q
Kinetics