Advertisements
Advertisements
प्रश्न
Derive an expression for maximum safety speed with which a vehicle should move along a curved horizontal road. State the significance of it.
उत्तर
- Consider a vertical section of a car moving on a horizontal circular track having a radius ‘r’ with ‘C’ as the centre of the track.
- Forces acting on the car (considered to be a particle):
a. Weight (mg), vertically downwards,
b. Normal reaction (N), vertically upwards that balances the weight
c. Force of static friction (fs) between the road and the tyres.
Since normal reaction balances the weight
∴ N = mg ...(1)
While working in the frame of reference attached to the vehicle, the frictional force balances the centrifugal force.
`f_s = (mv^2)/r` ...(2)
Dividing equation (2) by equation (1),
∴ `f_s/"N" = v^2/rg` ...(3) - However, fs has an upper limit (fs)max = µsN, where μs is the coefficient of static friction between the road and the tyres of the vehicle. This imposes an upper limit to the speed v.
At the maximum possible speed,
`(f_s)_max/N = µ_s = v_max^2/(rg)` ...[From equations (2) and (3)]
∴ `v_max = sqrt(µ_srg)`
This is an expression of maximum safety speed with which a vehicle should move along a curved horizontal road. - Significance: The maximum safe speed of a vehicle on a curve road depends upon friction between tyres and road, the radius of the curved road and acceleration due to gravity.
संबंधित प्रश्न
Answer in brief:
Why are curved roads banked?
On what factors does the frequency of a conical pendulum depend? Is it independent of some factors?
The coefficient of static friction between a coin and a gramophone disc is 0.5. Radius of the disc is 8 cm. Initially the center of the coin is 2 cm away from the center of the disc. At what minimum frequency will it start slipping from there? By what factor will the answer change if the coin is almost at the rim? (use g = π2m/s2)
Answer in Brief:
A flywheel used to prepare earthenware pots is set into rotation at 100 rpm. It is in the form of a disc of mass 10 kg and a radius 0.4 m. A lump of clay (to be taken equivalent to a particle) of mass 1.6 kg falls on it and adheres to it at a certain distance x from the center. Calculate x if the wheel now rotates at 80 rpm.
Starting from rest, an object rolls down along an incline that rises by 3 in every 5 (along with it). The object gains a speed of `sqrt10` m/s as it travels a distance of `5/3` m along the incline. What can be the possible shape/s of the object?
A big dumb-bell is prepared by using a uniform rod of mass 60 g and length 20 cm. Two identical solid spheres of mass 25 g and radius 10 cm each are at the two ends of the rod. Calculate the moment of inertia of the dumb-bell when rotated about an axis passing through its centre and perpendicular to the length.
Does the angle of banking depend on the mass of the vehicle?
During ice ballet, while in the outer rounds, why do the dancers outstretch their arms and legs.
A hollow sphere has a radius of 6.4 m. what is the minimum velocity required by a motorcyclist at the bottom to complete the circle.
A body weighing 0.5 kg tied to a string is projected with a velocity of 10 m/s. The body starts whirling in a vertical circle. If the radius of the circle is 0.8 m, find the tension in the string when the body is at the top of the circle.
Derive an expression for the kinetic energy of a rotating body with uniform angular velocity.
A railway track goes around a curve having a radius of curvature of 1 km. The distance between the rails is 1 m. Find the elevation of the outer rail above the inner rail so that there is no side pressure against the rails when a train goes around the curve at 36 km/hr.
What is a conical pendulum? Obtain an expression for its time period
A particle undergoes uniform circular motion. The angular momentum of the particle remains conserved about, ______
When a mass is rotating in a plane about a fixed point, its angular momentum is directed along, ______
Give any two examples of torque in day-to-day life.
What is the relation between torque and angular momentum?
What are the rotational equivalents for the physical quantities, (i) mass and (ii) force?
A flywheel rotates with uniform angular acceleration. If its angular velocity increases from `20pi` rad/s to `40pi` rad/s in 10 seconds. Find the number of rotations in that period.
A uniform metallic rod rotates about its perpendicular bisector with constant angular speed. If it is heated uniformly to raise its temperature to a certain value, its speed of rotation ______.
A wheel of radius 2 cm is at rest on the horizontal surface. A point P on the circumference of the wheel is in contact with the horizontal surface. When the wheel rolls without slipping on the surface, the displacement of point P after half rotation of wheel is ______.
A ring and a disc of different masses are rotating with the same kinetic energy. If we apply a retarding torque τ on the ring, it stops after completing n revolution in all. If the same torque is applied to the disc, how many revolutions would it complete in all before stopping?
What is the difference between rotation and revolution?
