Advertisements
Advertisements
Question
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)
Advertisements
Solution
Given:
μs = 0.8
r = 72 m
θ = 78°4'
g = 10 m/s2
tan θ = tan 78°4' = 5
Vmin = `sqrt("rg"[("tan "theta - mu_"s")/(1 + mu_"s" "tan "theta)])`
= `sqrt(72 xx 10((5 - 0.8)/(1 + 0.8 xx 5)))`
`= sqrt(720 xx 4.2/(4 + 1)`
`= sqrt(3024/5)`
`= sqrt(144 xx 4.2)`
= 12 × 2.049
= 24.588 m/s
= 88.52 km/h
This will be the lower limit or minimum speed on this track.
Since the track is heavily banked, θ > 45°, there is no upper limit or maximum speed on this track.
APPEARS IN
RELATED QUESTIONS
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?
Using energy conservation, along a vertical circular motion controlled by gravity, prove that the difference between the extreme tensions (or normal forces) depends only upon the weight of the objects.
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)
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 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 ____________.
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 ______.
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 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 ______.
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 ______.
What is banking of a road?
Why it is necessary banking of a road?
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.
A horizontal force of 0.5 N is required to move a metal plate of area 10−2 m2 with a velocity of 3 × 10−2m/s, when it rests on 0.5 × 10−3 m thick layer of glycerin. Find the coefficient of viscosity of glycerin.
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]
