Advertisements
Advertisements
प्रश्न
The radius of a circular track is 200 m. Find the angle of banking of the track, if the maximum speed at which a car can be driven safely along it is 25 m/sec.
Advertisements
उत्तर
Given:
v = 25 m/s,
r = 200 m,
g = 9.8 m/s2
To find:
Angle of banking (θ) = ?
Formula:
`tan theta = (v_max^2)/(rg)`
∴ `tan theta = ((25^2))/(200 xx 9.8)`
∴ `tan theta = 625/1960`
∴ `tan theta = 0.3189`
∴ θ = tan−1 (0.3189)
∴ θ = 17°41'
Therefore, the angle of banking of the track should be approximately 17°41' to allow a car to be driven safely along it at a maximum speed of 25 m/s.
APPEARS IN
संबंधित प्रश्न
A road is constructed part of a racing tracks to be designed with radius of curvature 72 m. We are not recommending the vehieles to drive faster than 216 kmph.. The coefficient of static friction between the tyres of a vehicle on this road is 0.8, will there be any lower speed limit? By how much can the upper speed limit exceed in this case?
(Given: r = 72 m, vo = 216 km/h, w = 10 m, θ = 78°4', h = 9.805 m)
A metallic ring of mass 1 kg has a moment of inertia 1 kg m2 when rotating about one of its diameters. It is molten and remolded into a thin uniform disc of the same radius. How much will its moment of inertia be, when rotated about its own axis.
A block of mass m is moving on rough horizontal surface with momentum p. The coefficient of friction between the block and surface is µ. The distance covered by the block before it stops is [g =acceleration due to gravity)
For a body moving with constant speed in a horizontal circle, which of the following remains constant?
A cyclist with combined mass 80 kg goes around a curved road with a uniform speed 20 m/s. He has to bend inward by an angle `theta` = tan-1 (0.50) with the vertical. The force of friction acting at the point of contact of tyres and road surface is______.
[g = 10 m/s2 ]
In the case of conical pendulum, if T is the tension in the string and θ is the semivertical angle of cone, then the component of tension which balances the centrifugal force in equilibrium position is ______.
A motorcyclist rides in a horizontal circle about central vertical axis inside a cylindrical chamber of radius 'r'. If the coefficient of friction between the tyres and the inner surface of chamber is 'µ', the minimum speed of motorcyclist to prevent him from skidding is ______.
('g' =acceleration due to gravity)
A particle moves along a circular path of radius 'r' with uniform speed 'V'. The angle described by the particle in one second is ______.
A flat curved road on highway has radius of curvature 400 m. A car rounds the curve at a speed of 24 m/s. The minimum value of coefficient of friction to prevent car from sliding is ______.
(take g = 10 m/s2)
A particle rotates in horizontal circle of radius ‘R’ in a conical funnel, with speed ‘V’. The inner surface of the funnel is smooth. The height of the plane of the circle from the vertex of the funnel is ______.
(g = acceleration due to gravity)
A particle executes uniform circular motion with angular momentum 'L'. Its rotational kinetic energy becomes half when the angular frequency is doubled. Its new angular momentum is ______.
What is banking of a road?
Why it is necessary banking of a road?
A curved road 5 m wide is to be designed with a radius of curvature 900 m. What should be the elevation of the outer edge of the road above the inner edge optimum speed of the vehicles rounding the curve is 30 m/s.
A cyclist is undertaking horizontal circles inside a cylindrical well of radius 5 m. If the friction coefficient is 0.5, what should be the minimum speed of the cyclist?
A string of length 0.5 m carries a bob of mass 0.1 kg at its end. If this is to be used as a conical pendulum of period 0.4 π sec, the angle of inclination of the string with the vertical is ______. (g = 10m/s2)
What about the kinetic friction between the road and the tyres?
The radius of curvature of road is 60 m. If angle of banking is 27°, find maximum speed with which vehicle can tum along this curve. . (g = 9.8 m/s2)
A body performing uniform circular motion has ______.
Why does a motorcyclist moving along a level curve at high speed have to lean more than a cyclist moving along the same curve at low speed?
Derive an expression for maximum speed moving along a horizontal circular track.
In case of well of death which is a vertical cylindrical wall of radius ‘r’ inside which vehicle is driven in horizontal circles. If ‘m’ is mass of vehicle, ‘V’ is the velocity and u, is the coefficient of static friction between the wheels of vehicle and walls then correct relation is ______.
[g = acceleration due to gravity]
