Master Key Physics - Part I (Std. XII)
14
Thin is th e r equi red e xpr es sio n fo r ma xi mum
is net possible. Action and reaction are a pair
safety speed.
of re al fo rc es w hic h ad on th e di ffe ren t p ad s of
t wo i n te r act ing bodi e s. Ce n tri pe t al forc e i s a r e al
Significance:
f orc e b ut ce n tri fug al forc e i s no t a r eal for ce. I t i s
( I ) T h e m a x i mu m s a f e sp e e d o f a v e h i d e o n a cu r v e d
the force acing on the same body that has to be
mad
introd uc ed in no n -in erfi al fra me o f m fer eno to
m a k e N ew ton ' s l aw s of mo ti on t ru e.
W h a t i s b a n k i n g o f ro a d s ? W h y i s i t n ec e s s a r y ?
0 mar ks(
Ans. The proc ess of
surface
of
(3)
tyres
a nd
If
th e
fric tion
is
no t
suf ficien t
to
pro vid e
c en hip e tal fo rce, t he v eh icle is l i ke ly to s ki d off
the road.
'Q24. Draw a diagram showing all components of
f o r c e s ac t i n g o n a v e h i cl e m o v i ng o n a cu r v e d
r o ad s . T h e a n gl e m a d e b y t h e
mad
betw een
r ai s in g o u ter e dg e o f r oa d
o v e r i ts i nn er edg e t hro ug h c e rt ai n a ngl e is kno wn
a s b a n k in g o f
f ri c ti o n
Friction depends on the nature of the surface and
p re s enc e o f oi l o r w at e r on th e r od.
1 . 7 Ba n ki n g o f R o ad s
. 0 .2 2
d ep e n d s u p on
r oa d.
(2)
w i th
the
hori zon tal
is
banked
call ed
rod.
th en ecessary
s i g n i fi c a nc e of e a c h t e r m i n v ol v e d i n i t . tO c t . a s
14 marks/
speed
and
state
"Sho w tha t th e an gle o f ba nki ng is ind epen den t
o f m a s s o f v e h ic l e .
r oa d sur f ace.
Ans.
force o f friction should b e i ncre as ed by m aking
r o a d s u r f ac e ro ug h. Th i s r ou s e s we a r a nd te a r
NN
o f t y r e s . T h e f o rc e o f fr i c ti o n i s a l s o n o t a lw a y s
reliable since it s value de x-rms., when road
surface beam,es wet or oily. One to this, to a void
I come
skidding of Ire car and for safety at high speeds,
b a n k i n g o f ro d s i s n e c e s s a r y .
1 0.23.
De ri v e th e e xp re s sion fo r ma xi mu m sa fe s pe ed
w i t h w h ic h v e h ic l e s ho u ld m o v e al o n g a c u r v e d
h ori zon t al ro ad. S ta t e i t ' s sig nific a nce. (2 ma r ks)
A n s . Co n s i d e r a v e h i cl e o f m a s s r e mo v i n g w i t h sp e e d
A
v along a curved horizont al road of r adius r.
The necessary centripe tal force for taking turn A
pro vid ed b y the fric t io n be tw e en th e t yro o f c ar
a nd ro ad s ur fac e.
it,N
/W he re p. i s co e ffici e nt of
static friction
mpzor
= Kmg
(mg)
FM.1.5 Circular motion of rehide on banked road.
From the fig
C e nt ri pe t al forc e = Forc e o f fric t ion
No rmal reofi on N= mg
o f ve hicl e]
AB = horizontal surface
A C = i n cl i n ed ro a d s u r fa c e
BC = height of outer edge of road above the inner
C.C. = centre of gravity of vehicle.
W = ( m g ) w e i g ht o f v e hi c l e
= angl e of banking
N = no rmal reaction
471
th e
OR
b y f o rc e o f f r ic t io n b e tw e e n t y r e s o f c a r an d t h e
In c a se o f a o r mo ving a t a high er s pe e d, th e
saf et y,
eq uatio n
for
I n c a se o f a ca r mo v ing alo ng a cu r ve d u nb an k ed
ro ad, th e nec es sar y c e nt ripe tal fo rc e is pro vid ed
maximu m
Wri te
angle o f b an king.
Let the surface of road makes an angle f with the
horizontal surface. It is called angle of banking.