CONCEPT MAP

LAWS OF MOTION
Chapter at a Glance

Newton’s Laws Of Motion

Newton's 1st Law or Law of Inertia- A body continues to be in its state of rest or in uniform motion along
a straight line unless an external force is applied on it. Mass is the measure of the inertia of the body.

Newton’s 2nd Law-The rate of change of linear momentum is proportional to the applied force and change in
momentum takes place in the direction of applied force.

Note :- Above result is not Newton’s second law rather it is the conditional result obtained from it,
under the condition when m = constant

Newton’s 3rd Law of Motion- For every action there is an equal and opposite reaction and both acts
on two different bodies F12 = – F21

If F12 is action then F21 reaction and if F21 is action then F12 reaction
 Linear Momentum - It is defined as the quantity of motion contained in the body. Mathematically it
is given by the product of mass and velocity. It is a vector quantity represented by, p = mv

Law of Conservation of Linear Momentum

If no external force acts on a system, then its total linear momentum remains conserved.

Impulse - Impulse received by the body during an impact is defined as the product of average impulsive
force and the short time duration for which it acts.

Impulsive Force - The force which acts on a body for very short duration of time but is still capable of
changing the position, velocity and direction of motion of the body up to large extent is known as impulsive
force.
Example -Force applied by foot on hitting a football, Force applied by boxer on a punching bag

Area enclosed under the impulsive force and time graph from t 1 to t2 gives the impulse imparted to the body from time t 1 to t2

Friction- The property by virtue of which the relative motion between two surfaces in contact is
opposed is known as friction

Types of Frictional Forces - Frictional forces are of three types :-

1. Static frictional force
2. Kinetic frictional force
3. Rolling frictional force
Static Frictional Force (fs) - Frictional force acting between the two surfaces in contact which are
relatively at rest, so as to oppose their relative motion, when they tend to move relatively under the effect of
applied force is known as static frictional force. Static friction opposes impending motion
The law of static friction is written as, 0 ≤ fs ≤ μsN

Limiting Friction- As the applied force F increases, fs also increases, remaining equal and opposite to the
applied force (up to a certain limit), thus keeping the body at rest is known as limiting friction. It is also
known as maximum value of static friction (f)s max

Kinetic Frictional Force (fk )- It is found experimentally that when relative motion has started, the
frictional force decreases from the static maximum value (f)s max , Frictional force that opposes relative
motion between surfaces in contact is called kinetic or sliding friction and is denoted by fk .
Experimentally, μk < μs

The variation of the force of friction with the applied force. When the block is at rest the force of friction (fs) balances the
applied force (F) until it reaches a maximum value (fs,max). As the applied force F increases, fs also increases, remaining
equal and opposite to the applied force (up to a certain limit), keeping the body at rest, after which the joint suddenly
breaks and the surfaces start moving relatively

Rolling Frictional Force (fr)- Frictional force which opposes the rolling of bodies (like cylinder, sphere,
ring etc.) over any surface is called rolling frictional force.
The value of rolling friction is given as fr = μrN

Experimentally, μr<< μk < μs

Equilibrium of Concurrent Forces
If the number of forces act at the same point, they are called concurrent forces. The condition or the given
body to be in equilibrium under the number of forces acting on the body is that these forces should produce
zero resultant.

Equilibrium under three concurrent forces F1, F2 and F3 requires that the vector sum of the three
forces is zero. F1 + F2 + F3 = 0

Circular Motion of a car on a Level Road

The maximum speed with which the car can turn safely, vmax = √𝝁𝑹𝒈

Circular Motion of Car on a Banked Road

 The maximum possible speed of a car on a banked road to avoid slipping

 The optimum velocity on a banked road to avoid wear and tear of the tyres

1 Mark Questions

1. Is a single isolated force possible nature? Explain.

2. Two blocks of masses m1 and m2 are connected by a light spring on a smooth horizontal surface. The two
masses are pulled apart & then released. What is the ratio of their acceleration
3. Two identical frictionless tracks , one gradual & other steep meet at a point from where two stones are
allowed to slide down from rest, one on each track. What is the ratio of the time taken by the stones to
reach the bottom.
4. It is difficult to start a motion than to maintain it. Why?
5. Why passengers are thrown forward when a speeding bus suddenly stops?
6. How does coefficient of friction change when the weight of the body is doubled?
7. A light spring balance hangs from the hook of the other light spring. A block of mass M hangs from the
frmer. What is the scale reading of the two balances. ?
8. A block is kept on a frictionless inclined surface with angle of inclination  . The surface is given an
acceleration a to keep the block at rest. Find a .
9. A particles move under the action of a force F in x-y plane, so that its linear momentum at time t is given
by Px = 2 cos t ,Py = 2 sin t . What is the magnitude of force and momentum.
10. Find the acceleration of a particle at t = 3s in a circle of radius 20 cm moving with speed given by
v=2t m/s

2 and 3 Mark Questions

1. State the law of conservation of linear momentum and derive it using Newton’s third law of motion.
2. Obtain an expression for the angle which a cyclist make with the vertical while taking a circular turn.
3. Define angle of friction and angle of repose and establish a relation between them.
4. A block of mass m1 = 4 kg on a smooth plane of angle 300 is connected by a cord over a small, frictionless
pulley to a second block of mass m2 = 5kg hanging vertically. Calculate the acceleration with which the
block moves and also the tension in the cord.
5. A light string passing over a smooth light pulley connects two blocks of masses m1 and m2 (vertically). If
the acceleration of the system is g/8, find the ratio of the two masses.
6. A horizontal force of 12 kgf pushes a block weighing 5 kgf against a vertical wall. The coefficient of static
friction between the wall, and the block is 0.5 and the coefficient of kinetic friction is.04. (a) Will the
block slide down against the wall ? Assume that the block was not moving initially. (b) Will the answer
change, if the block was initially Sliding?
7. A 20 kg cart, with a boy of mass 60 kg riding it, is moving with a speed of 2m/s. The boy jumps off the
cart What is the change in speed of the cart, if (a) the boy on hitting the ground is moving with the same
speed as the cart ? (b) not moving relative to the ground ? (c) moving with twice the initial speed of the
cart in same direction ?
8. A simple pendulum is suspended from the ceiling of length 1m has a bob of mass 100 g and speed of 1.4
m/s at the lowest point in its path. Find the tension in the string at this instant.
9. A hammer weighing 1 kg moving with the speed of 10 m s1 strikes the head of a nail driving it 10 cm into
a wall. Neglecting the mass of the nail, calculate (i) the acceleration during the impact (ii) the time interval
during the impact and (iii) the impulse.

10. A ball of mass 1 kg hangs in equilibrium from two strings OA and OB as shown. Find the tension in the
two strings.
 11. A body of mass 5kg initially at rest explodes into three fragments of masses in the ratio 1:1:3. The two
pieces of equal masses fly off perpendicular to each other with a speed of 30m/s. Find the velocity of the
heavier fragment .
12. The magnitude of force acting on a body varies with time as shown. Find the magnitude of impulse of the
force

(a) between 2s and 6s

(b) between 0 and 12s

5 Mark Questions
1. Why is banking of roads done? Obtain an expression for the maximum speed with which a vehicle can
safely negotiate a curved road banked at an angle Ɵ, give the coefficient of friction between the road and
the tyres is µ.
2. Define static friction, limiting friction and kinetic friction. Show graphically the variation of the force of
friction with the applied force and using the graph show that the static friction is a self adjusting force.
3. Show that the Newton’s second law is the real law of motion.

Case Study Based Questions

1. A boy of mass 50 kg is standing on a balance kept on the floor of an elevator of mass 2500kg. The elevator can
move up or down either with uniform velocity or uniform acceleration which can be adjusted to the required value .
The force exerted by the scale on the boy is indicated by the scale and is known as the apparent weight. This apparent
weight can be found by applying the Newton’s second law of motion. What will be the apparent weight of the boy if
(take g=10m/s2)

(a) The lift moves up with constant velocity of 4m/s

(i) 700N
(ii) 300N
(iii) 500N
(iv) None of the above
(b) The cable supporting the elevator breaks and the elevator starts falling down freely
(i) 500N
(ii) 400N
(iii) 300N
(iv) Zero
(c) The elevator accelerates up at the rate of 2m/s2
(i) 600N
(ii) 400N
(iii) 200N
 (iv) Zero
(d) If the supporting cable can withstand a maximum tension of 35700N, with what maximum
acceleration can the lift move?
(i) 2m/s2
(ii) 3m/s2
(iii) 4m/s2
(iv) 5m/s2
(e) The lift is moving down with acceleration a. The boy in the lift drops a ball inside the lift. The
acceleration as observed by the boy is( taking upward direction positive)
(i) -a
(ii) a-g
(iii) -g
(iv) -(g+a)

2. Centripetal acceleration of the body moving in a circle of radius R with uniform speed is v 2/R towards
the centre of the circle. For a car of mass m taking a circular turn of radius R on a level road with velocity v
, the centripetal force required for circular motion is provided by a component of the contact force( which is
the frictional force with coefficient of friction as µs) between the road and car tyres along the surface of the
road. Answer the following questions:

(a) In case this motion takes place on a banked road with angle Ɵ and assuming all other
parameters given above remain same:
(i) The car tyres will wear more on a banked road than on a level road.
(ii) The car tyres will wear less on a banked road than on a level road.
(iii) The wear of tyres will be same in two cases
(iv) The force of friction will not depend upon the Normal reaction in the two cases.

(b) In case the car takes a circular turn on a banked road vis-a vis on a level road
(i) Car cannot take a turn on a level road in the absence of friction force but can take a
turn on a banked road
(ii) Car will not be able to take turn both at level road and banked road in absence of
friction force
(iii) Car will be able to take a turn on a level road but cannot take a turn on a banked road
in the absence of friction force.
(iv) Car can take a turn on a level road as well as on a banked road even if there is no
friction force.
(v)
(c) Which of the following statement(s) is/are correct with regard to the optimum ( at which no
wear and tear of tyre takes place) and maximum permissible speeds ( to avoid slipping) of the
car taking a turn of radius R on a banked road with angle Ɵ :
(i) Optimum speed and maximum permissible speed of car will be same
(ii) Optimum speed will depend upon the coefficient of friction whereas the maximum
speed will depend only upon the angle of banking.
(iii) Optimum speed will depend upon the angle of banking whereas, the maximum
permissible speed will depend upon both the angle of banking and the coefficient of
friction.
(iv) Optimum speed will depend on the angle of banking whereas the maximum
permissible speed will depend on the coefficient of friction.
(d) A turn on a level road has a radius of 100 m. The maximum speed which a car can turn
without skidding if the coefficient of friction between the tyres and road is 0.8
(take g = 9.8 m/s2)
(i) 45 m/s
(ii) 28 m/s
(iii) 1 m/s
(iv) 89 m/s
(e) At Ɵ = 450 and µs= 0.5, the ratio of V(optimum) and V (max) will be :
 (i) 1/√3
(ii) √3
(iii) 1
(iv) 3

ASSERTION AND REASONING TYPE

Two statements are given – one labeled Assertion (A) and the other labeled as Reason (R). Select the
correct answer to these questions from the codes (a), (b), (c) and (d) as given below.
(a) Both A and R are true and R is the correct explanation of A
(b) Both A and R are true but R is NOT the correct explanation of A
(c) A is true but R is false
(d) A is false and R is also false

1. Assertion: Inertia is the property by virtue of which A body is unable to change its state of rest only.
Reason: The bodies do not change their state unless acted upon by an unbalancedexternal force.
2. Assertion: If the net external force on the body is zero, then its acceleration is zero.
Reason: Acceleration does not depend on force.
3. Assertion: Newton's second law of motion gives the measurement of force.
Reason: According to Newton's second law of motion, force is directly proportionalto the rate of change of
momentum.
4. Assertion: No force is required to move a body uniformly along a circle.
Reason: When the motion is uniform, acceleration is zero.
5. Assertion: Mass is a measure of inertia of the body in linear motion.
Reason: Greater the mass, greater is the force required to change its state of rest or ofuniform motion.
6. Assertion: The slope of momentum versus time curve give us the acceleration.
Reason: Acceleration is given by the rate of change of momentum.
7. Assertion: A cyclist always bends inwards while negotiating a curve.
Reason: By bending, cyclist lowers his centre of gravity.
8. Assertion: The work done in bringing a body down from the top to the base along africtionless incline
plane is the same as the work done in bringing it down the verticalside.
Reason: The gravitational force on the body along the inclined plane is the same asthat along the vertical
side.
9. Assertion: Linear momentum of a body changes even when it is moving uniformly in acircle.
Reason: Force required to move a body uniformly along a straight line is zero.
HOTS
1. Find the acceleration of two blocks as shown in figure. All surfaces are frictionless and strings and pulleys are
light.
2. A block of mass 2kg is placed on the floor. The coefficient of static friction is 0.4. A force of 2.5N is applied
on the block as shown. Calculate the force of friction between the block and the floor.3.

3. Find the tensions T 1 and T2 in the strings shown

4. The pulleys and strings shown in the figure are smooth and of negligible mass. Find the angle Ɵ for the
system to remain in equilibrium.