Advertisements
Advertisements
Question
A car moving at a speed of 36 km/hr is taking a turn on a circular road of radius 50 m. A small wooden plate is kept on the seat with its plane perpendicular to the radius of the circular road (In the following figure). A small block of mass 100 g is kept on the seat which rests against the plate. the friction coefficient between the block and the plate is. (a) Find the normal contact force exerted by the plate on the block. (b) The plate is slowly turned so that the angle between the normal to the plate and the radius of the road slowly increases. Find the angle at which the block will just start sliding on the plate.
Advertisements
Solution
Given :
Speed of the car = v = 36 km/h = 10 m/s
Radius of the road = r = 50 m
Friction coefficient between the block and the plate = μ = 0.58
Mass of the small body = m = 100 g = 0.1 kg
(a) Let us find the normal contact force (N) exerted by the plant of the block.
\[N = \frac{\text{mv}^2}{r} = 0 . 1 \times \frac{100}{50} = \frac{1}{5} = 0 . 2\]
(b) The plate is turned; so, the angle between the normal to the plate and the radius of the rod slowly increases.
Therefore, we have :
\[N = \frac{\text{mv}^2}{r}\text{ cos }\theta . . . \left(\text{ i }\right)\]
\[\mu N = \frac{m v^2}{r}\text{ sin }\theta . . . \](ii)
\[\text { On using i and ii , we get : } \]
\[\frac{\mu m v^2}{r}\cos\theta = \frac{\text{mv}^2}{r}\sin\theta\]
\[ \Rightarrow \mu = \text{ tan }\theta\]
\[ \Rightarrow \theta = \tan^{- 1} (0 . 58) \approx 30^\circ\]
APPEARS IN
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?
A 70 kg man stands in contact against the inner wall of a hollow cylindrical drum of radius 3 m rotating about its vertical axis with 200 rev/min. The coefficient of friction between the wall and his clothing is 0.15. What is the minimum rotational speed of the cylinder to enable the man to remain stuck to the wall (without falling) when the floor is suddenly removed?
A thin circular loop of radius R rotates about its vertical diameter with an angular frequency ω. Show that a small bead on the wire loop remains at its lowermost point for `omega <= sqrt(g/R)` .What is the angle made by the radius vector joining the centre to the bead with the vertical downward direction for `omega = sqrt("2g"/R)` ?Neglect friction.
A smooth block loosely fits in a circular tube placed on a horizontal surface. The block moves in a uniform circular motion along the tube. Which wall (inner or outer) will exert a nonzero normal contact force on the block?
A car moves at a constant speed on a road as shown in figure. The normal force by the road on the car NA and NB when it is at the points A and B respectively.
A particle is kept fixed on a turntable rotating uniformly. As seen from the ground the particle goes in a circle, its speed is 20 cm/s and acceleration is 20 cm/s2. The particle is now shifted to a new position to make the radius half of the original value. The new value of the speed and acceleration will be
Three identical cars A, B and C are moving at the same speed on three bridges. The car A goes on a place bridge, B on a bridge convex upward and C goes on a bridge concave upward. Let FA, FB and FC be the normal forces exerted by the car on the bridges when they are at the middle of bridges.
Let θ denote the angular displacement of a simple pendulum oscillating in a vertical plane. If the mass of the bob is m, the tension is the string is mg cos θ
Assume that the earth goes round the sun in a circular orbit with a constant speed of 30 kms
A person stands on a spring balance at the equator. By what fraction is the balance reading less than his true weight?
A car goes on a horizontal circular road of radius R, the speed increasing at a constant rate \[\frac{\text{dv}}{\text{dt}} = a\] . The friction coefficient between the road and the tyre is μ. Find the speed at which the car will skid.
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.
When seen from below, the blades of a ceiling fan are seen to be revolving anticlockwise and their speed is decreasing. Select the correct statement about the directions of its angular velocity and angular acceleration.
In non-uniform circular motion, the ratio of tangential to radial acceleration is (r = radius, a = angular acceleration and v = linear velocity)
Two particles A and B are located at distances rA and rB respectively from the centre of a rotating disc such that rA > rB. In this case, if angular velocity ω of rotation is constant, then ______
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 block of 200 g mass moves with a uniform speed in a horizontal circular groove, with vertical side walls of radius 20 cm. If the block takes 40 s to complete one round, the normal force by the side walls of the groove is ______.
Which of the following statements is FALSE for a particle moving in a circle with a constant angular speed?
Define centripetal force.
A particle at rest starts moving with constant angular acceleration ‘α’ in circular path. At what time the magnitude of centripetal acceleration is half the tangential acceleration?
