x2 t07 05 conical pendulum
DESCRIPTION
TRANSCRIPT
![Page 1: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/1.jpg)
The Conical Pendulum
![Page 2: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/2.jpg)
The Conical PendulumA
P
![Page 3: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/3.jpg)
The Conical PendulumA
h
rO P
![Page 4: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/4.jpg)
The Conical PendulumA Force Diagram
h
rO P
![Page 5: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/5.jpg)
The Conical PendulumA Force Diagram
h
rO P
![Page 6: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/6.jpg)
The Conical PendulumA Force Diagram
h
rO P
TT= tension in the string
(always away from object)
![Page 7: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/7.jpg)
The Conical PendulumA
mg
Force Diagram
h
rO P
TT= tension in the string
(always away from object)
![Page 8: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/8.jpg)
The Conical PendulumA
mg
Force Diagram
h
rO P
TT= tension in the string
(always away from object)
icalwith vertmakesstring
![Page 9: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/9.jpg)
The Conical PendulumA
mg
Force Diagram
h
rO P
TT= tension in the string
(always away from object)
icalwith vertmakesstring
pendulumoflocity angular ve
![Page 10: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/10.jpg)
The Conical PendulumA
mg
Force Diagram
h
rO P
TT= tension in the string
(always away from object)
icalwith vertmakesstring
pendulumoflocity angular ve
Resultant Forces
![Page 11: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/11.jpg)
The Conical PendulumA
rmvxm
2
mg
Force Diagram
h
rO P
TT= tension in the string
(always away from object)
icalwith vertmakesstring
pendulumoflocity angular ve
Resultant Forces
![Page 12: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/12.jpg)
The Conical PendulumA
rmvxm
2
0ym
mg
Force Diagram
h
rO P
TT= tension in the string
(always away from object)
icalwith vertmakesstring
pendulumoflocity angular ve
Resultant Forces
![Page 13: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/13.jpg)
The Conical PendulumA
rmvxm
2
0ym
mg
Force Diagram
h
rO P
TT= tension in the string
(always away from object)
icalwith vertmakesstring
pendulumoflocity angular ve
Resultant Forces
rmv2
forces horizontal
![Page 14: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/14.jpg)
The Conical PendulumA
rmvxm
2
0ym
mg
Force Diagram
h
rO P
TT= tension in the string
(always away from object)
icalwith vertmakesstring
pendulumoflocity angular ve
Resultant Forces
rmv2
forces horizontal 0forcesvertical
![Page 15: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/15.jpg)
The Conical PendulumA
rmvxm
2
0ym
mg
Force Diagram
h
rO P
TT= tension in the string
(always away from object)
icalwith vertmakesstring
pendulumoflocity angular ve
Resultant Forces
rmv2
forces horizontal
0forcesvertical
![Page 16: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/16.jpg)
The Conical PendulumA
rmvxm
2
0ym
mg
Force Diagram
h
rO P
TT= tension in the string
(always away from object)
icalwith vertmakesstring
pendulumoflocity angular ve
Resultant Forces
rmv2
forces horizontal
0forcesvertical
![Page 17: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/17.jpg)
The Conical PendulumA
rmvxm
2
0ym
mg
Force Diagram
h
rO P
TT= tension in the string
(always away from object)
icalwith vertmakesstring
pendulumoflocity angular ve
Resultant Forces
rmv2
forces horizontal
sinT
0forcesvertical
![Page 18: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/18.jpg)
The Conical PendulumA
rmvxm
2
0ym
mg
Force Diagram
h
rO P
TT= tension in the string
(always away from object)
icalwith vertmakesstring
pendulumoflocity angular ve
Resultant Forces
rmv2
forces horizontal
sinT
rmvT
2
sin
0forcesvertical
![Page 19: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/19.jpg)
The Conical PendulumA
rmvxm
2
0ym
mg
Force Diagram
h
rO P
TT= tension in the string
(always away from object)
icalwith vertmakesstring
pendulumoflocity angular ve
Resultant Forces
rmv2
forces horizontal
sinT
rmvT
2
sin 2mr
0forcesvertical
![Page 20: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/20.jpg)
The Conical PendulumA
rmvxm
2
0ym
mg
Force Diagram
h
rO P
TT= tension in the string
(always away from object)
icalwith vertmakesstring
pendulumoflocity angular ve
Resultant Forces
rmv2
forces horizontal
sinT
rmvT
2
sin 2mr
0forcesvertical
![Page 21: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/21.jpg)
The Conical PendulumA
rmvxm
2
0ym
mg
Force Diagram
h
rO P
TT= tension in the string
(always away from object)
icalwith vertmakesstring
pendulumoflocity angular ve
Resultant Forces
rmv2
forces horizontal
sinT
rmvT
2
sin 2mr
0forcesvertical
mgcosT
![Page 22: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/22.jpg)
The Conical PendulumA
rmvxm
2
0ym
mg
Force Diagram
h
rO P
TT= tension in the string
(always away from object)
icalwith vertmakesstring
pendulumoflocity angular ve
Resultant Forces
rmv2
forces horizontal
sinT
rmvT
2
sin 2mr
0forcesvertical
mgcosT
mgTmgT
cos0cos
![Page 23: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/23.jpg)
mgrmv
TT 1
cossin 2
![Page 24: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/24.jpg)
mgrmv
TT 1
cossin 2
rgv2
tan
![Page 25: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/25.jpg)
mgrmv
TT 1
cossin 2
rgv2
tan
gr 2
![Page 26: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/26.jpg)
mgrmv
TT 1
cossin 2
rgv2
tan
gr 2
hrAOP tan in But
![Page 27: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/27.jpg)
mgrmv
TT 1
cossin 2
rgv2
tan
gr 2
hrAOP tan in But
hr
rgv
2
![Page 28: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/28.jpg)
mgrmv
TT 1
cossin 2
rgv2
tan
gr 2
hrAOP tan in But
hr
rgv
2
2
2
vgrh
![Page 29: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/29.jpg)
mgrmv
TT 1
cossin 2
rgv2
tan
gr 2
hrAOP tan in But
hr
rgv
2
2
2
vgrh
2
g
![Page 30: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/30.jpg)
mgrmv
TT 1
cossin 2
rgv2
tan
gr 2
hrAOP tan in But
hr
rgv
2
2
2
vgrh
2
g
Implications
![Page 31: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/31.jpg)
mgrmv
TT 1
cossin 2
rgv2
tan
gr 2
hrAOP tan in But
hr
rgv
2
2
2
vgrh
2
g
Implications
•depth of the pendulum below A is independent of the length of the string.
![Page 32: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/32.jpg)
mgrmv
TT 1
cossin 2
rgv2
tan
gr 2
hrAOP tan in But
hr
rgv
2
2
2
vgrh
2
g
Implications
•depth of the pendulum below A is independent of the length of the string.
•as the speed increases, the particle (bob) rises.
![Page 33: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/33.jpg)
e.g. The number of revolutions per minute of a conical pendulum increases from 60 to 90.Find the rise in the level of the bob.
![Page 34: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/34.jpg)
e.g. The number of revolutions per minute of a conical pendulum increases from 60 to 90.Find the rise in the level of the bob.
![Page 35: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/35.jpg)
e.g. The number of revolutions per minute of a conical pendulum increases from 60 to 90.Find the rise in the level of the bob.
T
![Page 36: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/36.jpg)
e.g. The number of revolutions per minute of a conical pendulum increases from 60 to 90.Find the rise in the level of the bob.
mg
T
![Page 37: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/37.jpg)
e.g. The number of revolutions per minute of a conical pendulum increases from 60 to 90.Find the rise in the level of the bob.
mg
Th
r
![Page 38: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/38.jpg)
e.g. The number of revolutions per minute of a conical pendulum increases from 60 to 90.Find the rise in the level of the bob.
mg
Th
r
rmv2
forces horizontal
![Page 39: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/39.jpg)
e.g. The number of revolutions per minute of a conical pendulum increases from 60 to 90.Find the rise in the level of the bob.
mg
Th
r
rmv2
forces horizontal 0forcesvertical
![Page 40: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/40.jpg)
e.g. The number of revolutions per minute of a conical pendulum increases from 60 to 90.Find the rise in the level of the bob.
mg
Th
r
rmv2
forces horizontal 0forcesvertical
![Page 41: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/41.jpg)
e.g. The number of revolutions per minute of a conical pendulum increases from 60 to 90.Find the rise in the level of the bob.
mg
Th
r
rmv2
forces horizontal
sinT
0forcesvertical
![Page 42: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/42.jpg)
e.g. The number of revolutions per minute of a conical pendulum increases from 60 to 90.Find the rise in the level of the bob.
mg
Th
r
rmv2
forces horizontal
sinT2sin mrT
0forcesvertical
![Page 43: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/43.jpg)
e.g. The number of revolutions per minute of a conical pendulum increases from 60 to 90.Find the rise in the level of the bob.
mg
Th
r
rmv2
forces horizontal
sinT2sin mrT
0forcesvertical
![Page 44: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/44.jpg)
e.g. The number of revolutions per minute of a conical pendulum increases from 60 to 90.Find the rise in the level of the bob.
mg
Th
r
rmv2
forces horizontal
sinT2sin mrT
0forcesvertical
mg
cosT
![Page 45: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/45.jpg)
e.g. The number of revolutions per minute of a conical pendulum increases from 60 to 90.Find the rise in the level of the bob.
mg
Th
r
rmv2
forces horizontal
sinT2sin mrT
0forcesvertical
mg
cosT
mgTmgT
cos0cos
![Page 46: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/46.jpg)
gr
mgmr
2
2
1tan
![Page 47: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/47.jpg)
gr
mgmr
2
2
1tan
hr
tanBut
![Page 48: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/48.jpg)
gr
mgmr
2
2
1tan
hr
tanBut
2
2
gh
hr
gr
![Page 49: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/49.jpg)
gr
mgmr
2
2
1tan
hr
tanBut
2
2
gh
hr
gr
rad/s2
rad/s60
12060rev/minwhen
![Page 50: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/50.jpg)
gr
mgmr
2
2
1tan
hr
tanBut
2
2
gh
hr
gr
rad/s2
rad/s60
12060rev/minwhen
m4
2
2
2
g
gh
![Page 51: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/51.jpg)
gr
mgmr
2
2
1tan
hr
tanBut
2
2
gh
hr
gr
rad/s2
rad/s60
12060rev/minwhen
m4
2
2
2
g
gh
rad/s3
rad/s60
180rev/min09when
![Page 52: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/52.jpg)
gr
mgmr
2
2
1tan
hr
tanBut
2
2
gh
hr
gr
rad/s2
rad/s60
12060rev/minwhen
m4
2
2
2
g
gh
rad/s3
rad/s60
180rev/min09when
m9
3
2
2
g
gh
![Page 53: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/53.jpg)
gr
mgmr
2
2
1tan
hr
tanBut
2
2
gh
hr
gr
rad/s2
rad/s60
12060rev/minwhen
m4
2
2
2
g
gh
rad/s3
rad/s60
180rev/min09when
m9
3
2
2
g
gh
0.14m
m94
heightin rise 22
gg
![Page 54: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/54.jpg)
(ii) (2002)A particle of mass m is suspended by a string of length l from a point directly above the vertex of a smooth cone, which has a vertical axis. The particle remains in contact with the cone and rotates as a conical pendulum with angular velocity .
The angle of the cone at its vertex iswhere , and the string makes an
2
4
angle of with the horizontal as shown in the diagram. The forces acting on the particle are the tension in the string T, the normal reaction N and the gravitational force mg.
![Page 55: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/55.jpg)
(ii) (2002)A particle of mass m is suspended by a string of length l from a point directly above the vertex of a smooth cone, which has a vertical axis. The particle remains in contact with the cone and rotates as a conical pendulum with angular velocity .
The angle of the cone at its vertex iswhere , and the string makes an
2
4
angle of with the horizontal as shown in the diagram. The forces acting on the particle are the tension in the string T, the normal reaction N and the gravitational force mg.
Note: whenever a particle makes contact with a surface there will be a normal force perpendicular to the surface.
![Page 56: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/56.jpg)
a) Show, with the aid of a diagram, that the vertical component of N is sinN
![Page 57: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/57.jpg)
a) Show, with the aid of a diagram, that the vertical component of N is sinN
![Page 58: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/58.jpg)
a) Show, with the aid of a diagram, that the vertical component of N is sinN
T
![Page 59: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/59.jpg)
a) Show, with the aid of a diagram, that the vertical component of N is sinN
T
![Page 60: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/60.jpg)
a) Show, with the aid of a diagram, that the vertical component of N is sinN
NT
![Page 61: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/61.jpg)
a) Show, with the aid of a diagram, that the vertical component of N is sinN
NT
mg
![Page 62: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/62.jpg)
a) Show, with the aid of a diagram, that the vertical component of N is sinN
NT
![Page 63: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/63.jpg)
a) Show, with the aid of a diagram, that the vertical component of N is sinN
NT
![Page 64: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/64.jpg)
a) Show, with the aid of a diagram, that the vertical component of N is sinN
NT
![Page 65: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/65.jpg)
a) Show, with the aid of a diagram, that the vertical component of N is sinN
NT
mg
![Page 66: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/66.jpg)
a) Show, with the aid of a diagram, that the vertical component of N is sinN
NT
mg
c
![Page 67: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/67.jpg)
a) Show, with the aid of a diagram, that the vertical component of N is sinN
NT
mg
c
sin
sin
NcNc
![Page 68: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/68.jpg)
a) Show, with the aid of a diagram, that the vertical component of N is sinN
NT
mg
c
sin
sin
NcNc
sinisof component verticalthe
NN
![Page 69: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/69.jpg)
a) Show, with the aid of a diagram, that the vertical component of N is sinN
NT
mg
c
sin
sin
NcNc
sinisof component verticalthe
NN
and , of terms
in for expressionan find and ,sin
that Show b)
lm
NTmgNT
![Page 70: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/70.jpg)
a) Show, with the aid of a diagram, that the vertical component of N is sinN
NT
mg
c
sin
sin
NcNc
sinisof component verticalthe
NN
and , of terms
in for expressionan find and ,sin
that Show b)
lm
NTmgNT
2forces horizontal mr
![Page 71: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/71.jpg)
a) Show, with the aid of a diagram, that the vertical component of N is sinN
NT
mg
c
sin
sin
NcNc
sinisof component verticalthe
NN
and , of terms
in for expressionan find and ,sin
that Show b)
lm
NTmgNT
2forces horizontal mr
![Page 72: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/72.jpg)
a) Show, with the aid of a diagram, that the vertical component of N is sinN
NT
mg
c
sin
sin
NcNc
sinisof component verticalthe
NN
and , of terms
in for expressionan find and ,sin
that Show b)
lm
NTmgNT
2forces horizontal mr
cosT cosN
![Page 73: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/73.jpg)
a) Show, with the aid of a diagram, that the vertical component of N is sinN
NT
mg
c
sin
sin
NcNc
sinisof component verticalthe
NN
and , of terms
in for expressionan find and ,sin
that Show b)
lm
NTmgNT
2forces horizontal mr
cosT2coscos mrNT
cosN
![Page 74: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/74.jpg)
a) Show, with the aid of a diagram, that the vertical component of N is sinN
NT
mg
c
sin
sin
NcNc
sinisof component verticalthe
NN
and , of terms
in for expressionan find and ,sin
that Show b)
lm
NTmgNT
2forces horizontal mr
cosT2coscos mrNT
cosN
0forcesvertical
![Page 75: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/75.jpg)
a) Show, with the aid of a diagram, that the vertical component of N is sinN
NT
mg
c
sin
sin
NcNc
sinisof component verticalthe
NN
and , of terms
in for expressionan find and ,sin
that Show b)
lm
NTmgNT
2forces horizontal mr
cosT2coscos mrNT
cosN
0forcesvertical
![Page 76: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/76.jpg)
a) Show, with the aid of a diagram, that the vertical component of N is sinN
NT
mg
c
sin
sin
NcNc
sinisof component verticalthe
NN
and , of terms
in for expressionan find and ,sin
that Show b)
lm
NTmgNT
2forces horizontal mr
cosT2coscos mrNT
cosN
0forcesvertical
mgsinT sinN
![Page 77: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/77.jpg)
a) Show, with the aid of a diagram, that the vertical component of N is sinN
NT
mg
c
sin
sin
NcNc
sinisof component verticalthe
NN
and , of terms
in for expressionan find and ,sin
that Show b)
lm
NTmgNT
2forces horizontal mr
cosT2coscos mrNT
cosN
0forcesvertical
mgsinT
mgNTmgNT
sinsin0sinsin
sinN
![Page 78: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/78.jpg)
mgNT sinsin
![Page 79: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/79.jpg)
mgNT sinsin
sin
sinmgNT
mgNT
![Page 80: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/80.jpg)
mgNT sinsin
sin
sinmgNT
mgNT
2coscos mrNT
![Page 81: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/81.jpg)
mgNT sinsin
sin
sinmgNT
mgNT
2coscos mrNT
cos
cos2
2
mrNT
mrNT
![Page 82: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/82.jpg)
mgNT sinsin
sin
sinmgNT
mgNT
2coscos mrNT
cos
cos2
2
mrNT
mrNT
cosBut lr
![Page 83: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/83.jpg)
mgNT sinsin
sin
sinmgNT
mgNT
2coscos mrNT
cos
cos2
2
mrNT
mrNT
cosBut lr 2mlNT
![Page 84: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/84.jpg)
mgNT sinsin
sin
sinmgNT
mgNT
2coscos mrNT
cos
cos2
2
mrNT
mrNT
cosBut lr 2mlNT
and , of in terms of valuefor this expressionan Find cone. th thecontact wi lose about to is
particlewhen theis,that 0,untilincreasedislocity angular veThe c)
gl
N
![Page 85: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/85.jpg)
mgNT sinsin
sin
sinmgNT
mgNT
2coscos mrNT
cos
cos2
2
mrNT
mrNT
cosBut lr 2mlNT
and , of in terms of valuefor this expressionan Find cone. th thecontact wi lose about to is
particlewhen theis,that 0,untilincreasedislocity angular veThe c)
gl
N
;0When N
![Page 86: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/86.jpg)
mgNT sinsin
sin
sinmgNT
mgNT
2coscos mrNT
cos
cos2
2
mrNT
mrNT
cosBut lr 2mlNT
and , of in terms of valuefor this expressionan Find cone. th thecontact wi lose about to is
particlewhen theis,that 0,untilincreasedislocity angular veThe c)
gl
N
;0When N
sinmgT
![Page 87: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/87.jpg)
mgNT sinsin
sin
sinmgNT
mgNT
2coscos mrNT
cos
cos2
2
mrNT
mrNT
cosBut lr 2mlNT
and , of in terms of valuefor this expressionan Find cone. th thecontact wi lose about to is
particlewhen theis,that 0,untilincreasedislocity angular veThe c)
gl
N
;0When N
sinmgT 2 and mlT
![Page 88: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/88.jpg)
mgNT sinsin
sin
sinmgNT
mgNT
2coscos mrNT
cos
cos2
2
mrNT
mrNT
cosBut lr 2mlNT
and , of in terms of valuefor this expressionan Find cone. th thecontact wi lose about to is
particlewhen theis,that 0,untilincreasedislocity angular veThe c)
gl
N
;0When N
sinmgT 2 and mlT
2
sin
mlmg
![Page 89: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/89.jpg)
mgNT sinsin
sin
sinmgNT
mgNT
2coscos mrNT
cos
cos2
2
mrNT
mrNT
cosBut lr 2mlNT
and , of in terms of valuefor this expressionan Find cone. th thecontact wi lose about to is
particlewhen theis,that 0,untilincreasedislocity angular veThe c)
gl
N
;0When N
sinmgT 2 and mlT
2
sin
mlmg
sin
sin2
lg
lg
![Page 90: X2 T07 05 conical pendulum](https://reader034.vdocuments.mx/reader034/viewer/2022051313/549d0b88ac7959c42a8b48ed/html5/thumbnails/90.jpg)
Exercise 9C; all