Q.2- A car can be driven on flat circular road of radius r at a maximum speed v without skidding. The same car is now driving on another flat circular road of radius 2r on which the coefficient of friction between its Tyre and the road is the same as on the first road. What is the maximum speed of the car on the second road such that its does not skid?(Use v =√rusg formula).
Answers
For uniform circular motion, the resultant acceleration is
a
R
=
a
N
2
+a
t
2
a
N
=
R
v
2
,a
t
=
dt
dv
=a
From FBD of car on the rough road
f=ma
R
μN=m
(
R
v
2
)
2
+(
dt
dv
)
2
⇒μ
2
N
2
=m
2
(
R
2
v
4
+a
2
)
⇒v
4
=
m
2
μ
2
N
2
R
2
−a
2
R
2
=
m
2
μ
2
m
2
g
2
R
2
−a
2
R
2
=μ
2
g
2
R
2
−a
2
R
2
v=[(μ
2
g
2
−a
2
)R
2
]
4
1
.
solution
The maximum speed of the car on the second road that it does not skid is √2g
Explanation:
If the coefficient of friction is μ and its mass m
Then, the friction on the car will be
The centripetal force on the car when it is moving with speed v at the circular path of radius r
Both forces will be equal
Therefore,
Now when the car is travelling on circular road of radius 2r, if its speed is V
Then,
Therefore, the maximum speed of the car that it does not skid is √2g
Hope this answer is helpful.
Know More:
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