AUNITS AND MEASUREMENTS, ERRORS AND DIMENSIONAL ANALYSIS

Physics4-Newtons laws of motion, Friction and noninertial frame

LAWS OF MOTION

1.FIRST LAW OF MOTION

According to this law, every body continues in its state of rest or motion in a straight line unless it is compelled by external force to change that state.

(i)This law is also called law of inertia. Inertia is a virtue by which a body opposes the state of rest or motion.

(ii)Force is such a factor, which is essential for change in translatory motion of a body.

(iii)The first law of motion defines the force.

Examples :

(a)To remove the dust particles from a cloth by shaking it

(b) Banking of the passengers (towards the motion of bus), sitting in a bus on applying the sudden brakes.

2.SECOND LAW OF MOTION

According to this law, the rate of change of momentum (mass x velocity) of a body is proportional to the impressed force and it takes place in the direction of the force.

Mathematically

(Defining force such a way that k = 1)

=

In scalar form, F = ma

(i)Force is a vector quantity, whose unit is Newton or (in MKS) and Dyne or (I n C.G.S.)

(ii)The dimension of force is [MLT2]

(iii)The second law of motion gives the magnitude and unit of force.

(iv)If m is not constant

As in case of rocket propulsion, the mass of the fuel varies with respect to time.

3.THIRD LAW OF MOTION

According to this law, Every action has its equal and opposite reaction. When two bodies A and B exert force on each other, the force (action) of A on B

, is always equal and opposite to the force of B on A

Thus

(i)This law expresses the nature of force.

(ii)Action and reaction always acts on different bodies Impulse : If a force acts on a body for a short duration (t, then impulse is defined as product of force and its time of action

i.e. Impulse = Force x Duration (

By Newtons second law

When and are initial and final momenta of the body respectively. Thus impulse of force =. Graphically, the impulse is the area between the force curve and the F = 0 axis, as shown in figure. The SI unit of impulse is Ns. Graphical interpretation of impulse as area under the curve..

Friction Introduction (i)When two surfaces in contact have relative motion or have tendency of motion with each other then a force acts at the point of contact of the object and this force is called frictional force.

(ii)The force of friction is always in a direction opposite to which the body tends to move

(iii)It is parallel to the surface

(iv)Frictional force is independent of the area of surface in contact

(v)The force of friction depends on the nature of material of the surface contact,

(vi)Friction is a non conservative force i.e. work done against friction is path dependent.(vii)Generally many of us have a. misconception that friction opposes the motion of a moving body but it favours the motion of a body. It opposes the relative motion between the two bodies. When a person walks forward, he pushes the ground backward. The rough surface of ground exerts a forward force which causes the motion of the person.

TYPES OF FRICTIONFriction is of two types,

(a) Static friction

(b) Kinetic friction

Now let us have some discussion on these types of friction

Static friction

(i)Frictional force between two surfaces when there is no relative motion between them is called static friction.

(ii)Static friction is self adjusting in nature. It adjusts its magnitude in such a way that together with other forces applied on a body, it maintains relative rest between two surfaces.

(iii)The value of static friction lies between 0 and (s N i.e. 0 ( fs ( (sN where (s is coefficient of static friction and N is normal force.

(iv)There is no energy loss due to static friction. We may perform work against static friction or static friction may perform work.

Kinetic friction :(i)Frictional force between the, two surfaces which are in relative motion is called kinetic friction.

(ii)The magnitude of the kinetic friction is proportional to the normal force acting between the two surfaces i.e.fk ( N

fk = (kN where (k is coefficient of kinetic friction.

(iii)This force of kinetic friction always acts opposite to the direction of motion.

(iv)Work done against kinetic friction is conserved i.e. converted into heat. So in case of kinetic friction, there is always an energy loss

NOTE : If nothing is specified for (k and (s, then we assume that both are equal. Theoretically (k < (s

ANGLE OF FRICTIONThe angle of friction is defined as the angle which the resultant of the friction and normal reaction makes with the normal reaction, If ( is the angle of friction

But , coefficient of friction

( tan ( = (. Thus coefficient of static friction is equal to the tangent of the angle of friction.ANGLE OF REPOSEThe angle of repose is defined as the angle of the inclined plane at which a body placed on it begins to slide. In the equilibrium condition

F = mg sin (

N = Mg cos (On dividing one by other

Since

( ( = tan (Thus coefficient of limiting friction is equal to the tangent of angle of repose.EXERcise 1

Q1Find frictional force on block 30 kg

(A) 20 N

(B) 30 N

(C) 40 N

(D) 50 N

Q2The pulley and string shown in figure are smooth and of negligible mass. For the system to remain in equilibrium, the angle ( should be, (Given M = m)

(A) 0(

(B) 30 (

(C) 45 (

(D) 60 (Q3.A block of mass m is kept on an inclined plane of a lift moving down with acceleration of 2 m/s2. What should be the minimum coefficient of friction to let the block move down with constant velocity ?

(A)

(B)

(C)

(D)(=not defined

Q4From the fixed pulley, masses 2 kg, 1 kg and 3 kg are suspended as shown in the figure. Find the extension in the spring if k = 100 N/m.

(A) 0.1 m

(B) 0.2 m

(C) 0.3 m

(D) 0

Q5.The raindrops are hitting the back of a man walking at a speed of 5 km/hr. If he now starts running in the same direction with a constant acceleration, the magnitude of velocity of the rain with respect to him will

(A) gradually increase

(B) gradually decrease

(C) first decrease then increase

(D) first increase then decrease

Q6The floor of an elevator at rest at 10th floor of a building is a plane mirror. A particle is projected with a speed m/s and at 45( with the horizontal as shown in the figure. At the very instant of projection, the cable of the elevator breaks and the elevator starts falling freely. What will be the separation between the particle and its image 0.5 second after the instant, of projection?

(A) 0.5 m

(B) 1 m

(C) 2 m

(D) 1.5 m

Q7Motion of one, projectile as observed by another projectile if both are projected simultaneously is

(A) always a straight line

(B) a parabola

(C) a complicated curve

(D) a straight line or a parabola depending on their initial velocities

Q8.A boy throws a ball at an angle 45( with the horizontal and with a speed 20 m/sec. with respect to ground while standing on a car moving at 10 m/sec and accelerated at a m/s2. What should be the value of a so that the boy can catch the ball standing under it? (g = 10 m/sec2)

(A) 20 m/sec2

(B) 10 m/sec2

(C) 5 m/sec2

(D) none

Q9A particle is thrown horizontally with a speed of 10 m/s from the top of a cliff 15 m high above the ground. An inclined plane runs at an angle 45( with the horizontal as shown in the figure. At what height above the ground does the particle hit the plane? (Take g = 10 m/sec2)

(A) 5 m

(B) 10 m

(C) 4 m

(D) 6 m

Q10If the seat of a boy on a vertical merry go round revolving with a constant speed breaks up suddenly so that the boy starts falling, he will have a subsequent motion directed

(A)tangential to the direction of revolution.

(B)towards the centre of the merrygoround i.e. radially inwards.

(C)radially outwards.

(D)towards a direction not specified in either of (A), (B) and (C).

Q11If an external force starts acting on a moving particle, which of the following is not essentially true?

(A)The line of motion of the particle will keep changing.

(B)The speed of the particle will keep changing.

(C)The particle will keep moving.

(D)None is essentially true.

Q12An observer finds the magnitudes of the acceleration of two bodies to be the same. This necessary implies that the two bodies

(A)are at rest with respect to each other.

(B)are at rest or move with constant velocities with respect to each other.

(C)are accelerated with respect to each other.

(D)may be at rest, moving with constant velocities or accelerated with respect to other.

Q13For the v t plot of a particle in motion over a time period t3 seconds, what should be the distance traveled s vs time t plot like ?

(a)

(b)

(c)

(d)

Q14.In the system shown all surfaces are smooth. The acceleration of 5 kg will be (applied force is 1N down the incline )

(a) 10 m/s2

(b) m/s2

(c) m/s2

(d) None

Q15The system shown is in equilibrium. The minimum and maximum mass of the hanging block for equilibrium is

(a) 4.8 kg, 6.4 kg (b) 8 kg, 8kg

(c) 2.88 kg, 6.72 kg (d) None

Q16A block of mass m is placed on a smooth wedge of an angle ( The whole system is accelerated horizontally so that block does not slip on the wedge. The force exerted by the wedge on the block will be

(a) mg cos (

(b)

(c) mg sin (

(d) mg

Q17.In the system shown, a man of mass 50 kg climbs up the rope with an acceleration of 1 m/s2 relative to rope. The acceleration of 10 kg is

(a) 1 m/s2

(b) 7.5 m/s2

(c) 5 m/s2

(d) None

Q18.The value of time when 2 kg block starts sliding on 5 kg block, if time dependent force is applied on 2 kg block as shown

(a) never slides (b) 1 sec

(c) 1.4 sec

(d) None

Q19.The minimum force required to move the block up the incline is (m = 10 kg, ( = 0.5 ) is

(a) 60N

(b) 100 N

(c) 40N

(d) None

20.A block of mass of kg is fired with a speed of 5 m/s towards an ideal spring of constant k = 50 N/m. It compresses the spring by maximum of 20 cm. The speed with which it returns back to the point of projections is [coefficient of friction (= ]

(a) 5 m/s

(b) 2 m/s

(c) will not return (d) 1 m/s

Q21.A uniform rope of mass 5 kg is moved up a smooth incline plane by using a force F = 50 N. The tension in the rope at its mid point is

(a) 20 N

(b) 25 N

(c) 50 N

(d) None

Q22.System shown is pushed in such a way that 1 kg block remains stationary relative to 10 kg block. The minimum acceleration required for this purpose is

(a) 10 m/s2

(b) 20 m/s2

(c) any acceleration (d) None

Q23.The acceleration of wedge is 5 m/s2 right. What is the acceleration of block

(a) 5 m/s2

(b) 10 m/s2

(c) 2.5 m/s2

(d) 7.5 m/s2

Q24.Two blocks are placed one over the another and system is placed on a rough horizontal surface as shown

The acceleration of 4 kg block and 2 kg block is

(a) 0, 0

(b) 0, m/s2

(c) m/s2,m/s2(d) None

Q25. A 40 kg slab rests on a frictionless floor. A 10 kg block rests on top of the slab [Fig.] The static coefficient of friction between the block and the slab is 0.60 while the kinetic coefficient is 0.40. The 10 kg block is acted upon by a horizontal force of 100 N. If g = 9.8 m/S2 the resulting acceleration of the slab will be:

(a) 0.98 m/s2

(b) 1.47m/s2

(c) 1.52 m/s2

(d) 6.1 m/s2

Q26.A mass m rests on a horizontal surface. The coefficient of friction between the mass and the surface is g. If the mass is pulled by a force F as shown in Fig. the limiting friction between mass and the surface will be:

(a) (mg

(b) ([mg ((3/2)F]

(c) ([mg (F/2)](d) ([mg + (F/2)]

Q27A lineman of mass 60 kg is holding a vertical pole. The coefficient of static friction between his hands and the pole is 0.5. If he is able to climb up the pole. What is the minimum force with which he should press the pole with his hands? (g = 10 m/s2)

(a) 1200 N

(b) 600 N

(c) 300 N

(d) 150 N

Q28Two steel balls A and B are placed inside a right circular cylinder of diameter 54 cm making contacts at points P, Q and R as shown. The radius rA = 12 cm and rB = 18 cm. The masses are mA = 15 kg and mB = 60 kg. The forces exerted by the floor at the point Q and the wall at R are, respectively (taking g = 10 m/s2):

(a) 600 N, 150 N(b) 750 N, 150 N(c) 600 N, 200 N(d) 750N,200N

Q29An elevator starts from rest with a constant upward acceleration. It moves 2 m in the first 0.6 second. A passenger in the elevator is holding a 3 kg package by a vertical string. When the elevator is moving, what is the tension in the string:

(a) 4 N

(b) 62.7 N

(c) 29.4 N

(d) 20.6 N

Q30A heavy spherical ball is constrained in a frame as shown in Fig. The inclined surface is smooth. Determine the maximum acceleration with which the frame can move without causing the ball to leave the frame.

(a)

(b)

(c)

(d)

Exercise 2

Q1In a situation the contact force by a rough horizontal surface on a body placed on it has constant magnitude. If the angle between this force and the vertical is decreased, the frictional force between the surface and the body will

(A) increase

(B) decreases

(C) remain the same(D) may increase or decrease

Q2While walking on ice, one should take small steps to avoid, slipping. This is because smaller steps ensure

(A) larger friction

(B) smaller friction

(C) larger normal force

(D) smaller normal force

Q3A block of mass 2 kg is placed on the floor. The coefficient of static friction is 0.4. If a force of 2.8 N is applied on the block parallel to floor the force of friction between the block and floor (taking g = 10m/s2) is

(A) 2.0 N

(B) 6 N

(C) 2 N

(D) zero

Q4 For the arrangement shown in fig., the tension in the string to prevent it from sliding down, is

(A) 6N

(B) 6.4 N

(C) 0.4 N

(D) None

Q5A body of mass 2 kg rests on a rough inclined plane making an angle 30( with the horizontal. The coefficient of static friction between the block and the plane is 0.7. The frictional force on the block is

(A) 9.8 N

(B) 0.7 x 9.8N(C) 9.8 x N

(D) 0.7 x 9.8 N

Q6.Block A of mass m rests on the plank B of mass 3 m which is free to slide on a frictionless horizontal surface. The coefficient of friction between the block ad plank is 0.2. If a horizontal force of magnitude 2mg is applied to the plank B, the acceleration of A relative to the plank and relative to the ground respectively, are:

(a) 0,

(b) 0,

(c) ,

(d) ,

Q7.A block of mass m is given an initial downward velocity v0 and left on an inclined plane (coefficient of friction = 0.6). The block will:

(a) continue to move down the plane with constant velocity v0

(b) accelerate downward

(c) decelerate and come to rest

(d) first accelerate downward and then decelerate and come to rest

Q8.For the arrangement shown in the figure, the tension in the string is given by

(a) 30 N

(b) 40 N

(c) 116 N

(d) 4 N

Q9.A block is gently placed on a conveyor belt moving horizontally with constant speed. After t = 4s, the velocity of the block becomes equal to the velocity of the belt. If the coefficient of friction between the block and the belt is ( = 0.2, then the velocity of the conveyor belt is:

(a) 2 ms1

(b) 4 ms1

(c) 64 ms1

(d) 8 ms1Q10.A body is projected up a 45( rough incline. If the coefficient of friction is 0.5, then the retardation of the block is:

(a)

(b)

(c)

(d)

Q11.For the arrangement shown in figure, the tension in the string to prevent it from sliding down, is:

(a) 6 N

(b) 6.4 N

(c) 0.4 N

(d) zero

Q12.A body of mass 10 kg is placed on rough surface, pushed by a force F making an angle of 30( to the horizontal. If the angle of friction is also 30( then the minimum magnitude of force F required to move the body is equal to : (take g = 10 m/s2)

(a) 100 N

(b) N

(c) N

(d) 50 N

Q13.In the figure shown if coefficient of friction is (, then m2 will start moving upwards if:

(a) = sin ( ( cos (

(b) > sin ( + ( cos (

(c) = ( sin ( cos (

(d) = ( sin ( + cos (Q14.The coefficient of friction between the tyres and road is 0.4. The minimum distance covered before attaining a speed of 8 ms1 starting from rest is nearly : (g = 10 m/s2)

(a) 8.0 m

(b) 4.1 m

(c) 16.4 m

(d) 18.3 m

Q15.A block has been placed on an inclined plane. The slope angle ( of the plane is such that the block slides down the plane at a constant speed. The coefficient of kinetic friction is equal to:

(a) sin (

(b) cos (

(c) g

(d) tan (Q16.A block of mass M rests on a rough horizontal surface as shown. Coefficient of friction between the block and the surface is (. A force F = Mg acting at angle ( with the vertical side of the block pulls it. In which of the following cases the block can be pulled along the surface:

(a) tan ( ( (

(b) tan( (

(c) cot ( ( (

(d) cot( (Q17.A body is released from the top of a smooth inclined plane of inclination (. It reaches the bottom with velocity v. If the angle of inclination is doubled, what will be the velocity of the body on reaching the ground:

(a) v

(b) 2v

(c) [2 cos (]1/2 v

(d) [2 sin (]1/2 vQ18.A box of mass 8 kg is placed on a rough inclined plane of inclination (. Its downward motion can be prevented by applying an upward pull F. And it can be made to slide upwards by applying a force 2F. The coefficient of friction between the box and the inclined plane is:

(a) tan (

(b) 3 tan (

(c) tan (

(d) 2 tan (Q19.A block is placed on the top of a smooth inclined plane of inclination ( kept on the floor of a lift. When the lift is descending with a retardation a, the block is released. The acceleration of the block relative to the incline is:

(a) g sin (

(b) a sin (

(c) (g a) sin (

(d) (g + a) sin (Q20.The upper half of an inclined plane of inclination ( is perfectly smooth while the lower half rough. A block starting from rest at the top of the plane will again come to rest at the bottom if the coefficient of friction between the block and the lower half of the plane is given by:

(a) ( = 2 tan (

(b) ( = tan (

(c) ( =

(d) ( =

Q21.A block of mass M is sliding down the plane. Coefficient of static friction is (s and kinetic friction is (k. Then friction force acting on the block is:

(a) (s Mg cos (

(b) (F + mg) sin (

(c) (k (F + Mg) cos (

(d) (Mg + F) tan (Q22.In the arrangement shown in figure, there is a friction force between the blocks of masses m and 2m. The mass of the suspended block is m. The block of mass m is stationary with respect to block of mass 2m. The minimum value of coefficient of friction between m and 2m is:

(a) 1/2

(b)

(c) 1/4

(d) 1/3

Q23.A block of mass 10 kg is placed at a distance of 5 m from the rear end of a long trolley as shown in figure. The coefficient of friction between the block and the surface is 0.2. Starting from rest, the trolley is given a uniform acceleration of 3 ms2. At what distance from the starting point will the block fall off the trolley?

(Take g = 10 ms2)

(a) 10 m

(b) 20 m

(c) 25 m

(d) 30 mQ24.A block of mass m is placed on another block of mass M which itself is lying on a horizontal surface. The coefficient of friction between two blocks is (1 and that between the block of mass M and horizontal surface is (2. What maximum horizontal force can be applied to the lower block so that the two blocks move without separation:

(a) (M + m) ((2 (1)g

(b) (M m) ((2 (1)g

(c) (M m) ((2 + (1)g

(d) (M + m) ((2 + (1)g

Q25.A block of mass 1 kg is placed on a truck which accelerates with acceleration 5 m/s2. The coefficient of static friction between the block and truck is 0.6. The frictional force acting on the block is:

(a) 5 N

(b) 6 N

(c) 5.88 N

(d) 4.6 N

Q26.A block of mass 10 kg is placed on a rough horizontal surface having coefficient of friction ( = 0.5. If a horizontal force of 100 N is applied on it, then the acceleration of the block will be

(a) 15 m/s2

(b) 10 m/s2

(c) 5 m/s2

(d) 0.5 m/s2Q27.If the coefficient of friction of a plane inclined at 30( is 0.4, then the acceleration of the body sliding freely on it, is: (g = 9.8 m/s2)

(a) 1.51 m/s2

(b) 3.54 m/s2

(c) 9.8 m/s2

(d) 4.9 m/s2Q28.A rough vertical board has an acceleration a along the horizontal so that a block of mass M pressing against it does not fall. The coefficient of friction between block and the board is:

(a)

(b)

(c)

(d)

Q29.A block is moving up an inclined plane of inclination ( = 30( with a velocity 5 m/s. If it stops after 0.5 sec then what is the value of coefficient of friction (():

(a) 0.6

(b) 0.5

(c) 1.25

(d) none

Q30.A car is moving along a straight horizontal road with a speed v0. If the coefficient of friction between the tyres and the road is (. The shortest distance in which the car can be stopped is:

(a)

(b)

(c)

(d)

Exercise 1 ANSWER KEY

Q1bQ2cQ3.aQ4cQ5bQ6.b

Q7aQ8.aQ9bQ10dQ11dQ12d

Q13dQ14.dQ15cQ16bQ17.bQ18.c

Q19.cQ20.dQ21.bQ22.bQ23.aQ24.b

Q25.aQ26.cQ27aQ28dQ29bQ30c

Exercise 2 ANSWER KEY

Q1bQ2bQ3aQ4 dQ5aQ6.d

Q7.cQ8.bQ9.dQ10.aQ11.dQ12.d

Q13.bQ14.aQ15.dQ16.dQ17.cQ18.a

Q19.dQ20.aQ21.cQ22.cQ23.aQ24.d

Q25.aQ26.cQ27.aQ28.dQ29.aQ30.d

EMBED PBrush

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