Advertisements
Advertisements
Question
You may have seen in a circus a motorcyclist driving in vertical loops inside a ‘death-well’ (a hollow spherical chamber with holes, so the spectators can watch from outside). Explain clearly why the motorcyclist does not drop down when he is at the uppermost point, with no support from below. What is the minimum speed required at the uppermost position to perform a vertical loop if the radius of the chamber is 25 m?
Advertisements
Solution 1
When the motorcyclist is at the highest point of the death-well, the normal reaction R on the motorcyclist by the ceiling of the chamber acts downwards. His weight mg also acts downwards. These two forces are balanced by the outward centrifugal force acting on him
:. `R + mg = (mv^2)/r` ......(1)
Here v is the speed of the motorcyclist and m is the mass of the motorcyclist (including the mass of the motorcycle). Because of the balancing of the forces, the motorcyclist does not fall down.
The minimum speed required to perform a vertical loop is given by equation (1) when R = 0.
`:. mg = mv_"min"^2` or `v_"min"^2 = gr`
or `v = sqrt(gr) = sqrt(10xx25) ms^(-1) = 15.8 ms^(-1)`
Solution 2
In a death-well, a motorcyclist does not fall at the top point of a vertical loop because both the force of normal reaction and the weight of the motorcyclist act downward and are balanced by the centripetal force. This situation is shown in the following figure.
The net force acting on the motorcyclist is the sum of the normal force (FN) and the force due to gravity (Fg = mg).
The equation of motion for the centripetal acceleration ac, can be written as:
Fnet = mac
`F_N + F_g= ma_c`
`F_N + mg =- (mv^2)/r`
Normal reaction is provided by the speed of the motorcyclist. At the minimum speed (vmin), FN = 0
`mg = mv_"min"^2`
`:.V_min = sqrt(rg)`
`= sqrt(25xx10) = 15.8` m/s
RELATED QUESTIONS
A disc revolves with a speed of `33 1/3` rev/min, and has a radius of 15 cm. Two coins are placed at 4 cm and 14 cm away from the centre of the record. If the co-efficient of friction between the coins and the record is 0.15, which of the coins will revolve with the record?
Tow cars having masses m1 and m2 moves in circles of radii r1 and r2 respectively. If they complete the circle in equal time, the ratio of their angular speed ω1/ω2 is
Water in a bucket is whirled in a vertical circle with string attached to it. The water does no fall down even when the bucket is inverted at the top of its path. We conclude that in this position
A coin placed on a rotating turntable just slips. If it is placed at a distance of 4 cm from the centre. If the angular velocity of the turntable is doubled, it will just slip at a distance of
A train A runs from east to west and another train B of the same mass runs from west to east at the same speed along the equator. A presses the track with a force F1 and B presses the track with a force F2.
Find the acceleration of the moon with respect to the earth from the following data:
Distance between the earth and the moon = 3.85 × 105 km and the time taken by the moon to complete one revolution around the earth = 27.3 days.
Find the acceleration of a particle placed on the surface of the earth at the equator due to earth's rotation. The diameter of earth = 12800 km and it takes 24 hours for the earth to complete one revolution about its axis.
A person stands on a spring balance at the equator. By what fraction is the balance reading less than his true weight?
A track consists of two circular parts ABC and CDE of equal radius 100 m and joined smoothly as shown in figure. Each part subtends a right angle at its centre. A cycle weighing 100 kg together with the rider travels at a constant speed of 18 km/h on the track. (a) Find the normal contact force by the road on the cycle when it is at B and at D. (b) Find the force of friction exerted by the track on the tyres when the cycle is at B, C and. (c) Find the normal force between the road and the cycle just before and just after the cycle crosses C. (d) What should be the minimum friction coefficient between the road and the tyre, which will ensure that the cyclist can move with constant speed? Take g = 10 m/s2.
What is the radius of curvature of the parabola traced out by the projectile in the previous problem at a point where the particle velocity makes an angle θ/2 with the horizontal?
In a certain unit, the radius of gyration of a uniform disc about its central and transverse axis is `sqrt2.5`. Its radius of gyration about a tangent in its plane (in the same unit) must be ______.
In non-uniform circular motion, the ratio of tangential to radial acceleration is (r = radius, a = angular acceleration and v = linear velocity)
A body slides down a smooth inclined plane having angle θ and reaches the bottom with velocity v. If a body is a sphere, then its linear velocity at the bottom of the plane is
A particle of mass m is performing UCM along a circle of radius r. The relation between centripetal acceleration a and kinetic energy E is given by
The escape velocity of a body from any planet, whose mass is six times the mass of earth and radius is twice the radius of earth will be
(v8 = escape velocity of a body from the earth's surface).
If a cyclist doubles his speed while negotiating a curve, how does the tendency to overturn vary?
A body of M.I. 2 kg m2 rotates with an angular velocity of 20 rad/s. When an external torque of 0.5 N m acts on it in the opposite direction, the number of revolutions it makes before it comes to rest is ____________.
A body is moving along a circular track of radius 100 m with velocity 20 m/s. Its tangential acceleration is 3 m/s2 then its resultant accelaration will be ______.
An engine is moving on a c1rcular path of radius 200 m with speed of 15 m/s. What will be the frequency heard by an observer who is at rest at the centre of the circular path, when engine blows the whistle with frequency 250 Hz?
A racing car travels on a track (without banking) ABCDEFA (Figure). ABC is a circular arc of radius 2 R. CD and FA are straight paths of length R and DEF is a circular arc of radius R = 100 m. The co-efficient of friction on the road is µ = 0.1. The maximum speed of the car is 50 ms–1. Find the minimum time for completing one round.
