Advertisements
Advertisements
प्रश्न
Answer in Brief:
Part of a racing track is to be designed for curvature of 72m. We are not recommending the vehicles to drive faster than 216 kmph. With what angle should the road be tilted? By what height will its outer edge be, with respect to the inner edge if the track is 10 m wide?
Advertisements
उत्तर
Given:
The radius of curvature of the track = 72m
Maximum speed = 216km/h = 60m/s
Width of the track = 10m
To find:
- The angle the road should be tilted by
- Height of the outer edge wrt inner edge
Solution:
The angle of banking of the road is given by
`tanθ = "v"^2/(rg)`
`θ = tan^-1("v"^2/(rg))`
θ = `tan^-1(60^2/(72 xx 10))`
θ = `tan^-1(3600/720)`
θ = `tan^-1(5)` = 78.69°
The height of the outer edge of the road is given by
`sinθ = h/w`
h = w sinθ
h = 10 × sin(78.69)
h = 10 × 0.9805
h = 9.805m
- The angle that the road should be tilted is 78.69°.
- The height of the outer edge is 9.805m.
APPEARS IN
संबंधित प्रश्न
Answer in brief:
A uniform disc and a hollow right circular cone have the same formula for their M.I. when rotating about their central axes. Why is it so?
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)
During a stunt, a cyclist (considered to be a particle) is undertaking horizontal circles inside a cylindrical well of radius 6.05 m. If the necessary friction coefficient is 0.5, how much minimum speed should the stunt artist maintain? The mass of the artist is 50 kg. If she/he increases the speed by 20%, how much will the force of friction be?
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.
Using the energy conservation, derive the expressions for the minimum speeds at different locations along a vertical circular motion controlled by gravity. Is zero speed possible at the uppermost point? Under what condition/s?
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)
A vehicle of mass m is moving with momentum p on a rough horizontal road. The coefficient of friction between the tyres and the horizontal road is µ. The stopping distance 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 ]
A horizontal circular platform of mass 100 kg is rotating at 5 r.p.m. about vertical axis passing through its centre. A child of mass 20 kg is standing on the edge of platform. If the child comes to the centre of platform then the frequency of rotation will become ______.
A car moves at a speed of 36 km hr-1 on a level road. The coefficient of friction between the tyres and the road is 0.8. The car negotiates a curve of radius R. If g = 10 ms-2 , then the car will skid (or slip) while negotiating the curve, if the value of R is ____________.
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 ______.
In the case of conical pendulum, if 'T' is the tension in the string and 'θ' is the semi-vertical angle of cone, then the component which provides necessary centripetal force 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)
The two blocks, m = 10 kg and M = 50kg are free to move as shown. The coefficient of static friction between the blocks is 0.5 and there is no friction between M and the ground. A minimum horizontal force F is applied to hold m against M that is equal to ______.
If friction is made zero for a road, can a vehicle move safely on this road?
Why it is necessary banking of a road?
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)
Write 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)
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.
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.
