Advertisements
Advertisements
प्रश्न
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
उत्तर १
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)`
उत्तर २
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
संबंधित प्रश्न
A stone of mass 0.25 kg tied to the end of a string is whirled round in a circle of radius 1.5 m with a speed of 40 rev/min in a horizontal plane. What is the tension in the string? What is the maximum speed with which the stone can be whirled around if the string can withstand a maximum tension of 200 N?
A motorcycle is going on an overbridge of radius R. The driver maintains a constant speed. As the motorcycle is ascending on the overbridge, the normal force on it
A simple pendulum having a bob of mass m is suspended from the ceiling of a car used in a stunt film shooting. the car moves up along an inclined cliff at a speed v and makes a jump to leave the cliff and lands at some distance. Let R be the maximum height of the car from the top of the cliff. The tension in the string when the car is in air is
A scooter weighing 150 kg together with its rider moving at 36 km/hr is to take a turn of a radius 30 m. What horizontal force on the scooter is needed to make the turn possible ?
A mosquito is sitting on an L.P. record disc rotating on a turn table at \[33\frac{1}{3}\] revolutions per minute. The distance of the mosquito from the centre of the turn table is 10 cm. Show that the friction coefficient between the record and the mosquito is greater than π2/81. Take g =10 m/s2.
The bob of a simple pendulum of length 1 m has mass 100 g and a speed of 1.4 m/s at the lowest point in its path. Find the tension in the string at this instant.
Suppose the bob of the previous problem has a speed of 1.4 m/s when the string makes an angle of 0.20 radian with the vertical. Find the tension at this instant. You can use cos θ ≈ 1 − θ2/2 and SINθ ≈ θ for small θ.
Suppose the amplitude of a simple pendulum having a bob of mass m is θ0. Find the tension in the string when the bob is at its extreme position.
A block of mass m is kept on a horizontal ruler. The friction coefficient between the ruler and the block is μ. The ruler is fixed at one end and the block is at a distance L from the fixed end. The ruler is rotated about the fixed end in the horizontal plane through the fixed end. (a) What can the maximum angular speed be for which the block does not slip? (b) If the angular speed of the ruler is uniformly increased from zero at an angular acceleration α, at what angular speed will the block slip?
In a children's park a heavy rod is pivoted at the centre and is made to rotate about the pivot so that the rod always remains horizontal. Two kids hold the rod near the ends and thus rotate with the rod (In the following figure). Let the mass of each kid be 15 kg, the distance between the points of the rod where the two kids hold it be 3.0 m and suppose that the rod rotates at the rate of 20 revolutions per minute. Find the force of friction exerted by the rod on one of the kids.
A particle is moving in a radius R with constant speed v. The magnitude of average acceleration after half revolution is ____________.
A rope is wound around a solid cylinder of mass 1 kg and radius 0.4 m. What is the angular acceleration of cylinder, if the rope is pulled with a force of 25 N? (Cylinder is rotating about its own axis.)
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 acceleration will be ______.
A body of mass m is performing a UCM in a circle of radius r with speed v. The work done by the centripetal force in moving it through `(2/3)`rd of the circular path is ______.
In negotiating curve on a flat road, a cyclist leans inwards by an angle e with the vertical in order to ______.
A racing car is travelling along a track at a constant speed of 40 m/s. A T.V. cameraman is recording the event from a distance of 30 m directly away from the track as shown in the figure. In order to keep the car under view in the position shown, the angular speed with which the camera should be rotated is ______.
Statement I: A cyclist is moving on an unbanked road with a speed of 7 kmh-1 and takes a sharp circular turn along a path of radius of 2 m without reducing the speed. The static friction coefficient is 0.2. The cyclist will not slip and pass the curve. (g = 9.8 m/s2)
Statement II: If the road is banked at an angle of 45°, cyclist can cross the curve of 2 m radius with the speed of 18.5 kmh-1 without slipping.
In the light of the above statements, choose the correct answer from the options given below.
Which of the following statements is FALSE for a particle moving in a circle with a constant angular speed?
