Lecture 3 : Equilibrium of a particle ; Static and kinetic friction ; Law of friction

A rectangular box lies on a rough inclined surface. The co-efficient
of friction between the surface and the box is μ. Let the mass of the
box be m.
(a) At what angle of inclination θ of the plane to the horizontal will
the box just start to slide down the plane?
(b) What is the force acting on the box down the plane, if the angle
of inclination of the plane is increased to α > θ ?
(c) What is the force needed to be applied upwards along the plane
to make the box either remain stationary or just move up with
uniform speed?
(d) What is the force needed to be applied upwards along the plane
to make the box move up the plane with acceleration a?

A cricket bowler releases the ball in two different ways
(a) giving it only horizontal velocity, and
(b) giving it horizontal velocity and a small downward velocity.
The speed vs at the time of release is the same. Both are released
at a height H from the ground. Which one will have greater speed
when the ball hits the ground? Neglect air resistance.

When a body slides down from rest along a smooth inclined plane
making an angle of 45° with the horizontal, it takes time T. When
the same body slides down from rest along a rough inclined plane
making the same angle and through the same distance, it is seen
to take time pT, where p is some number greater than 1. Calculate
the co-efficient of friction between the body and the rough plane.

A 100 kg gun fires a ball of 1kg horizontally from a cliff of height
500m. It falls on the ground at a distance of 400m from the bottom
of the cliff. Find the recoil velocity of the gun.

A block of mass M is held against a rough vertical wall by
pressing it with a finger. If the coefficient of friction between
the block and the wall is μ and the acceleration due to
gravity is g, calculate the minimum force required to be
applied by the finger to hold the block against the wall ?

In the above given problem if the lower thread is
pulled with a jerk, what happens?

A woman throws an object of mass 500 g with a speed of 25 m s1.
(a) What is the impulse imparted to the object?
(b) If the object hits a wall and rebounds with half the original speed,
what is the change in momentum of the object?

Why does a child feel more pain when she falls down on a hard
cement floor, than when she falls on the soft muddy ground in the
garden?

Two blocks of masses m₁, m₂ are connected by light spring on a smooth horizontal

surface. The two masses are pulled apart and then released. Prove that the ratio of

their acceleration is inversely proportional to their masses.

Name the factor on which coefficient of friction depends?

Force of 16N and 12N are acting on a mass of 200kg in mutually perpendicular
directions. Find the magnitude of the acceleration produced?

Friction is a self adjusting force. Justify. [

Why does a swimmer push the water backwards?

Why is it desired to hold a gun tight to one’s shoulder when it is being fired?

How does banking of roads reduce wear and tear of the tyres?

A thief jumps from the roof of a house with a box of weight W on his head. What
will be the weight of the box as experienced by the thief during jump?

Ten one rupee coins are put on top of one another on a table. Each coin has a mass
m kg. Give the magnitude and direction of
(a) The force on the 7th coin (counted from the bottom) due to all coins above it.
(b) The force on the 7th coin by the eighth coin and
(c) The reaction of the sixth coin on the seventh coin.

A lift is accelerated upward. Will the apparent weight of a person inside the lift
increase, decrease or remain the same relative to its real weight? If the lift is going
with uniform speed, then?

If force is acting on a moving body perpendicular to the direction of motion,
then what will be its effect on the speed and direction of the body?

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 ω ≤√g/R. What is the angle made by the radius vector joining the centre to the bead with the vertical downward direction for ω = √2g/R? Neglect friction.

 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?

 A disc revolves with a speed of 100 / 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 monkey of mass 40 kg climbs on a rope (Fig. 5.20) which can stand a maximum tension of 600 N. In which of the following cases will the rope break: the monkey
(a) climbs up with an acceleration of 6 m s^–2
(b) climbs down with an acceleration of 4 m s^–2
(c) climbs up with a uniform speed of 5 m s^–1
(d) falls down the rope nearly freely under gravity?
(Ignore the mass of the rope).

Two masses 8 kg and 12 kg are connected at the two ends of a light inextensible string that goes over a frictionless pulley. Find the acceleration of the masses, and the tension in the string when the masses are released.

Two bodies of masses 10 kg and 20 kg respectively kept on a smooth, horizontal surface are tied to the ends of a light string. A horizontal force F = 600 N is applied to (i) A, (ii) B along the direction of string. What is the tension in the string in each case?

A body of mass 0.40 kg moving initially with a constant speed of 10 m s^–1 to the north is subject to a constant force of 8.0 N directed towards the south for 30 s. Take the instant the force is applied to be t = 0, the position of the body at that time to be x = 0, and predict its position at t = –5 s, 25 s, 100 s.

The driver of a three-wheeler moving with a speed of 36 km/h sees a child standing in the middle of the road and brings his vehicle to rest in 4.0 s just in time to save the child. What is the average retarding force on the vehicle? The mass of the three-wheeler is 400 kg and the mass of the driver is 65 kg.

A body of mass 5 kg is acted upon by two perpendicular forces 8 N and 6 N. Give the magnitude and direction of the acceleration of the body.

One end of a string of length l is connected to a particle of mass m and the other to a small peg on a smooth horizontal table. If the particle moves in a circle with speed v the net force on the particle (directed towards the centre) is:
(i) T, (ii) T - mv² / l, (iii) T + mv² / l, (iv) 0
T is the tension in the string. 
[Choose the correct alternative]. 

 Give the magnitude and direction of the net force acting on
(a) a drop of rain falling down with a constant speed,
(b) a cork of mass 10 g floating on water,
(c) a kite skillfully held stationary in the sky,
(d) a car moving with a constant velocity of 30 km/h on a rough road,
(e) a high-speed electron in space far from all material objects, and free of electric and magnetic fields.