00:00see today we will start banking off-road
00:04what will we start? Banking off-road
00:07we will start, see in banking off-road
00:12we will first tell about banking off-road on smooth surface
00:17yes banking off-road we are telling that, banking off-road means
00:22when any body, car, bike or any vehicle
00:27turns on a turn, so the turn
00:31we call it banking, what do we call it?
00:34banking, the turn there
00:38the road there is inclined, how is it?
00:41inclined, it is on theta angle
00:44if you have any doubt, you can ask
00:46you?
00:48you can ask
00:51no
00:52see here
00:54when any vehicle, see here we have taken a car
00:57it will turn on a turn, when it will turn on a turn
01:00it will become a circular path
01:03when it will turn on a circular path
01:05so the road here is a little inclined
01:08it is on theta angle
01:12so what is the velocity?
01:14the relation between velocity and angle
01:16we will tell that in this
01:18so see here the diagram we have taken
01:21in this, there is a car
01:23when the car will turn on a turn
01:25so its velocity will be V
01:27and a normal reaction
01:31here I have taken its center C
01:33and the radius of this circular path
01:37will be R
01:39so here we will do its component
01:41what all forces will be applied on this?
01:45we are drawing FBD
01:47FBD of M
01:49draw it
01:53this will be MG
01:55in this direction
01:57we will take normal reaction
01:59this will be theta angle
02:03and
02:07we will do two components of this
02:09here this will be centripetal acceleration
02:11AC
02:13this is mass
02:15see here
02:17when we will do two components
02:19of normal reaction
02:21this will come in this direction
02:23n cos theta
02:25and in this direction
02:27n sin theta
02:29no problem
02:31n cos theta
02:33will be equal to MG
02:35because in this direction
02:37there is no acceleration in vertical
02:39so the equation
02:41n cos theta
02:43will be equal to MG
02:47and
02:49n sin theta
02:51is giving centripetal acceleration
02:53n sin theta
02:55is equal to
02:57M into
02:59AC
03:01we will write first equation
03:03and second equation
03:05if you have any problem
03:07you can ask
03:09see here n cos theta
03:11here normal reaction
03:13we will take perpendicular to plane
03:15this will be normal reaction
03:17in this direction n cos theta
03:19will be one component
03:21and here
03:23n sin theta
03:25n sin theta will provide centripetal
03:27acceleration
03:29so n sin theta
03:31will be equal to M into AC
03:33and n cos theta will be equal to MG
03:35no doubt
03:37now divide these two equations
03:39first and second
03:41divide
03:43in first equation
03:45divide in second equation
03:47n sin theta
03:49divided by
03:51n cos theta
03:53is equal to M into AC
03:55and this will be equal to MG
03:57see we will not teach much today
03:59we will teach little
04:01we will complete
04:03banking off road
04:05see here
04:07M is cancelled from M
04:09normal reaction is cancelled
04:11here sin theta upon cos theta
04:13what is it?
04:15tan theta
04:17is it or not?
04:19any problem?
04:21no
04:23AC is not value of
04:25centripetal acceleration
04:27P square by
04:29very good
04:31you tell
04:37P square by
04:39R
04:41this formula will be
04:43here this relation
04:45you have to remember
04:47in banking off road
04:49this tan theta value
04:51is
04:59tan theta
05:01is equal to
05:03V square by R
05:05you have to remember this formula
05:07in banking off road
05:09we will apply this
05:11any doubt?
05:13R is radius of circular path
05:15V is speed by which
05:17body is moving on circular turn
05:19that is V velocity
05:21and G is acceleration due to gravity
05:23any doubt?
05:25you don't have?
05:27no one?
05:29very good
05:31see we have taken
05:33this question
05:35this is the question
05:41you are not smart
05:43study
05:47you will not study
05:49very good
05:51you don't know smartness
05:53you did right or wrong
05:55radius of the curve
05:57road on
05:59national highway
06:01is R
06:03radius is
06:05R
06:07radius of third road
06:09is R
06:11width of road is
06:13B
06:15width of road is
06:17B
06:19outer edge
06:21of the road
06:23is raised by
06:25H with respect to
06:27inner edge
06:33so
06:35in respect to inner edge
06:37outer edge height
06:39will be more
06:41how much?
06:43H
06:45with respect to inner edge
06:47so that a car
06:49with velocity V can pass
06:51safely over it
06:53so if there is a car
06:55cross it safely with speed
06:57means
06:59there should not be accident
07:01so
07:03we have to find
07:05value of H
07:07so first of all
07:09we make a diagram
07:11this is road
07:13this is theta angle
07:19width of road is
07:21B
07:23height is
07:25H
07:27ok
07:29now
07:31in this car will pass
07:33its velocity is V
07:35from here we will make a car
07:37pass
07:41this car is passing
07:43its velocity is V
07:45so the radius of
07:47circular path of V
07:49will be
07:51radius R
07:53any problem?
07:55so here the formula is
07:57tan theta
07:59is equal to
08:01V square by
08:03RG
08:05this formula was told
08:07few minutes ago
08:09tan theta is
08:11perpendicular upon
08:13base
08:15tan theta is
08:17hypotenuse
08:19from here
08:21when we write tan theta
08:23how much we will write?
08:25tan theta is equal to H
08:27and base will be B
08:33from here question asked
08:35value of height
08:37so height H will be
08:39P square
08:43P
08:47upon
08:49RG
08:51you know
08:53you said
08:57so this height will be
08:59P square
09:01by RG
09:03I hope you will not have any problem
09:09move ahead
09:13ok this question
09:15you try to solve
09:23a guy holds a pendulum
09:25in his hand
09:27while standing at the edge
09:29of a circular
09:31platform of
09:33radius R
09:35rotating with an angular
09:37speed omega
09:41let us leave this
09:43for later
09:45let us
09:47study banking
09:49ok
09:51this was told
09:53on smooth surface
09:55now
09:57we are going to take
09:59rough surface
10:01what kind of surface?
10:03rough surface
10:05where
10:07there is friction
10:09here we will take
10:11rough surface
10:13motion of object
10:15on rough inclined circular
10:17path
10:19when a body moves
10:21on inclined circular path
10:23in that condition
10:25its motion will be
10:27velocity
10:29from minimum velocity
10:31to maximum velocity
10:33in range of velocity
10:35we can do anything
10:37clear
10:39rough
10:41circular path
10:43from minimum velocity
10:45to maximum velocity
10:47on any velocity
10:49you can pass any excuse
10:51no doubt
10:53no
10:55now you have to see
10:57what is the value
10:59to cross safely
11:01what will be Vmax
11:03maximum velocity
11:05will be when
11:07centripetal force
11:09friction centripetal
11:11force
11:13will be supported
11:15hello
11:17support
11:19here
11:21body is moving
11:23here
11:25friction is taken
11:27down the plane
11:29in two directions
11:31one is down the plane
11:33second
11:35up the plane
11:37away from the center
11:39and down the plane
11:41will be
11:43towards
11:45center
11:47that is why
11:49friction is taken
11:51down the plane
11:53because we need
11:55maximum velocity
11:57maximum
11:59yes
12:01towards center
12:03centripetal force is supported
12:05by friction
12:07yes
12:09normal reaction
12:11downward
12:13mg
12:15diagram
12:17fbd
12:19yes
12:21it is difficult
12:23difficult
12:25means
12:27it is difficult
12:29you have to pay attention
12:31this is
12:33theta
12:35this is normal
12:37this angle is also theta
12:39and here
12:41in this direction
12:43this normal reaction
12:45will have one component
12:47in this direction n
12:49cos theta and in this direction
12:51n sin theta
12:53I hope there will be no problem
12:55friction fs limiting
12:57we have put in this direction
12:59where we have put fs
13:01limiting
13:03this angle is theta
13:05so what will be this angle
13:07so according to this
13:09what will be this angle
13:11theta
13:13means fs
13:15friction's one component
13:17will come in this direction
13:19fs limiting
13:21cos theta will come in this direction
13:23and fs limiting
13:25sin theta
13:27will come in this direction
13:29and this
13:31will be in this direction
13:33centripetal axis
13:35this is a beautiful diagram
13:37n cos theta
13:39this is normal reaction's component
13:41will be in this direction
13:43n sin theta will come in this direction
13:45friction fs limiting
13:47down the plane
13:49one component of this
13:51fs limiting cos theta will come in this direction
13:53left
13:55second one will be downward
13:57fs limiting
13:59sin theta
14:01now here we will equal their components
14:03so here
14:05n cos theta
14:07will be
14:09mg plus fs limiting
14:11sin theta
14:13no problem
14:15n cos theta
14:17is equal to
14:19n cos theta
14:21is equal to
14:23mg plus fs limiting
14:25sin theta
14:27fs limiting value is
14:29mu s into
14:31n
14:33so this is mg
14:35plus mu s
14:37into n
14:39sin theta
14:43and here is n
14:45cos theta
14:47mu s into n sin theta
14:49transfer it
14:51left side
14:53so this will be n cos theta
14:55minus mu s
14:57into n
14:59sin theta is equal to
15:01mg
15:03here take n common
15:05we will get normal reaction's value
15:07cos theta
15:09minus mu s
15:11sin theta
15:13is equal to
15:15mg
15:17from here normal reaction's value will be
15:23mg divided by
15:25cos theta minus mu s
15:27sin theta
15:29if you have any problem, you can ask
15:31there is no question
15:33till now
15:35say
15:41now see second question
15:43n sin theta
15:45hello
15:53n sin theta
15:55plus fs limiting
15:59cos theta
16:01will be m into ac
16:03see
16:05n sin theta
16:07this component
16:09n sin theta and fs limiting
16:11cos theta
16:13this is centripetal acceleration
16:15m into ac
16:17no problem
16:19put the value
16:21n sin theta
16:23fs limiting's value
16:25mu s into
16:27n
16:29ok
16:31and
16:33this is
16:35cos theta
16:37this will be
16:39mg square upon r
16:41this is v max
16:43here take n common
16:49sin theta plus
16:51mu s
16:53cos theta
16:55this is m v max square
16:57upon r
16:59we have found value of n
17:01put it
17:05write it
17:07first equation and second equation
17:15pi equation first and
17:17second put it
17:19instead of n
17:21mg divided by
17:23cos theta
17:25what happened
17:29very easy
17:31cos theta minus mu s
17:33sin theta
17:35and above
17:37it is written
17:39sin theta plus
17:43mu s
17:45cos theta
17:47this is m v max
17:49square
17:51upon r
17:55cancel m
17:57multiply r
18:01maximum value of v
18:03maximum velocity
18:05body
18:07inclined plane
18:09maximum velocity
18:11no doubt
18:13you
18:15sawrab
18:17how much
18:19v max value
18:23under root
18:25r g
18:27in the bracket
18:29see this
18:31sin theta plus mu s
18:33cos theta
18:35sin theta plus
18:37mu s
18:39cos theta
18:41cos theta minus
18:43mu s sin theta
18:45this is the value
18:47ok
18:49see this is
18:51maximum value of v
18:53from this maximum velocity
18:55any body
18:57circular
18:59banking of road
19:01means curve
19:03from this maximum velocity
19:05any body can move
19:07from this maximum velocity
19:09any body can turn
19:11from this maximum velocity
19:13what will happen
19:15centipetal force
19:17required
19:19car will turn
19:21from this maximum velocity
19:23car will not turn
19:25that is why
19:27in highway
19:29it is written
19:31from this maximum velocity
19:33you should not drive
19:35more speed
19:37more speed
19:39keep driving
19:43ok
19:45take care
19:47ok
19:49ok
19:51ok
19:53ok
19:55ok
20:03ok
20:05write
20:07fast
20:09where are you lost
20:15done
20:17yours
20:19where are you lost
20:23now see
20:25find minimum velocity
20:27what to find
20:29v
20:31minimum value
20:33velocity
20:35circular path
20:37maximum
20:39minimum
20:41friction
20:43limiting
20:45away from the center
20:47down the plane
20:49friction
20:51up the plane
20:55centipetal force
20:57support
20:59for minimum
21:01we will make
21:03FVD
21:05what will be the force
21:07mg
21:09downward
21:11normal reaction
21:13perpendicular
21:15and the friction
21:17in this direction
21:19FS limiting
21:21ok
21:29ok
21:31ok
21:35ok
21:37ok
21:39ok
21:41ok
21:43ok
21:45ok
21:47ok
21:49ok
21:51ok
21:53ok
21:55ok
21:57ok
21:59ok
22:11ok
22:13ok
22:15ok
22:17for fs-limiting
22:21for fs-limiting
22:25for fs-limiting
22:29for fs-limiting
22:33for fs-limiting
22:37for fs-limiting
22:41for fs-limiting
22:45for fs-limiting
22:49for fs-limiting
22:53for fs-limiting
22:57for fs-limiting
23:01for fs-limiting
23:05for fs-limiting
23:09for fs-limiting
23:13for fs-limiting
23:17for fs-limiting
23:21for fs-limiting
23:25for fs-limiting
23:29for fs-limiting
23:33for fs-limiting
23:37for fs-limiting
23:41for fs-limiting
23:45for fs-limiting
23:49for fs-limiting
23:53for fs-limiting
23:57for fs-limiting
24:01for fs-limiting
24:05for fs-limiting
24:09for fs-limiting
24:13for fs-limiting
24:17for fs-limiting
24:21for fs-limiting
24:25for fs-limiting
24:29for fs-limiting
24:33for fs-limiting
24:37common
24:45sine theta
24:49sine theta
24:53sine theta
24:57mu s
25:31cos theta plus mu s sin theta
25:37and this is sin theta minus mu s cos theta
25:48this will be mv minimum square by r
25:52so from here m to am is cancelled
25:56multiply r here
26:00from here v minimum square value will be
26:05rg in the bracket
26:08sin theta minus mu s cos theta
26:14divided by cos theta plus mu s sin theta
26:22we will get v minimum and take its root
26:26shall we play?
26:34tell me what is the value of v minimum
26:37under root
26:40rg in the bracket
26:43sin theta minus mu s cos theta
26:50divided by
26:53cos theta plus mu s sin theta
26:59if you have any doubt, you can ask
27:03you?
27:05not at all?
27:07very good
27:11this is the minimum value of v
27:14on rough inclined plane
27:16and what we have found before is
27:18the maximum value of v
27:23means the overall value of v
27:26minimum and maximum
27:29is a range
27:32we will write it
27:35if you have noted it, then tell me
27:38have you done?
27:41so the value of v
27:53the minimum value of v is
27:56under root
27:59rg in the bracket
28:04sin theta minus mu s cos theta
28:11divided by cos theta
28:15plus mu s sin theta
28:19tell me
28:22what is the maximum value of v?
28:25under root
28:28rg
28:31sin theta plus mu s
28:34cos theta divided by
28:37cos theta minus mu s
28:41sin theta
28:49here
28:52sin theta plus mu s cos theta
28:55divided by cos theta minus mu s sin theta
28:58is v max or v minimum
29:01overall, the minimum value of v will be this
29:04and what will be the maximum value of v?
29:07between this minimum and maximum
29:10you can drive a car at any speed
29:13any vehicle, car, truck
29:16if you are driving on the road
29:19no problem, you will cross safely
29:22how will you cross?
29:25your vehicle will not turn
29:28even if you slow down, it will turn
29:31and
29:34even if you speed up, it will turn
29:37yes, the accident will be big in speeding
29:40but in slowing down
29:43yes
29:46overall, you have to remember
29:49whenever you turn on the road
29:52you have to drive between v minimum
29:55and v max
29:58you don't have to be over smart
30:01it is not a normal road
30:04you can drive at any speed
30:07any doubt?
30:11say that
30:14no?
30:17yes, that's all for today
30:20tomorrow we will start vertical circular motion
30:23we will start
30:26vertical circular motion
30:29we will discuss about it tomorrow
30:32that's all for today
Comments