Physics Chapter – 2 : Motion, force and laws of motion
12 August, 2024
Introduction: Motion, force and laws of motion
AReference Point is used to describe the location of an object. An object can be referred through many reference points.
Origin –
The reference point that is used to describe the location of an object is called Origin.For Example, a new restaurant is opening shortly at a distance of 5 km north from my house. Here, the house is the reference point that is used for describing where the restaurant is located.
What is motion?
If the location of an object changes with time the object is said to be in motion.
Distance: The magnitude of the length covered by a moving object is called distance. It has no direction.
Displacement: It is the shortest distance between two points or the distance between the starting and final positions with respect to time. It has magnitude as well direction. Displacement can be zero, but distance cannot.
Negative Displacement and Positive Displacement
Here, displacement of object B is negative ΔB = Bf − B0 = 7–12 = – 5 A negative sign indicates opposite direction here. Also, displacement of object A is positive ΔA = Af − A0 = 7– 0 = 7
Scalar and Vector Quantities
A vector quantity describes the magnitude as well as the direction.
A scalar quantity describes a magnitude or a numerical value.
Difference between distance and displacement
Distance
Displacement
Distance provides the complete details of the path taken by the object
Displacement does not provide the complete details of the path taken by the object
Distance is always positive
Displacement can be positive, negative and zero
It is a scaler quantity
It is a vector quantity
The distance between two points may not be unique
Displacement between two points is always unique
Uniform motion – When an object travels equal distances in equal intervals of time the object is said to have a uniform motion.
Non-uniform motion- When an object travels unequal distances in equal intervals of time the object is said to have a non-uniform motion.
Average Speed – If the motion of the object is non-uniform then we calculate the average speed to signify the rate of motion of that object.
Velocity- To describe the rate of motion in a direction the term velocity is used. It is defined as the speed of an object in a particular direction.
Velocity= Displacement/Time SI Unit: meters Symbol Representation: M/s or ms^(-1)
Instantaneous speed and instantaneous velocity
The magnitude of speed or velocity at a particular instance of time is called Instantaneous Speed or Velocity.
In case of uniform motion the velocity of an object remains constant with change in time. Hence, the rate of change of velocity is said to be zero.
Acceleration
In case of non-uniform motion the velocity of an object changes with time. This rate of change of velocity per unit time is called Acceleration. Acceleration= Change in velocity/ Time taken SI Unit: m/s2
Uniform Acceleration – An object is said to have a uniform acceleration if , It travels along a straight path and Its velocity changes (increases or decreases) by equal amounts in equal time intervals.
Non – Uniform Acceleration – An object is said to have a non-uniform acceleration if, Its velocity changes (increases or decreases) by unequal amounts in unequal time intervals.
Acceleration is also a vector quantity. The direction of acceleration is the same if the velocity is increasing in the same direction. Such acceleration is called Positive Acceleration.
The direction of acceleration becomes opposite as that of velocity if velocity is decreasing in a direction. Such acceleration is called Negative Acceleration.
De-acceleration or Retardation – Negative acceleration is also called De-acceleration or Retardation.
Graphical Representation of Motion
1. Distance – Time Graph
It represents a change in position of the object with respect to time.
The graph in case theobject is stationary (means the distance is constant at all time intervals) – Straight line graph parallel to x = axis
The graph in case of uniform motion – Straight line graph
The graph in case of non-uniform motion – Graph has different shapes
2. Velocity – Time Graphs
Constant velocity – Straight line graph, velocity is always parallel to the x-axis
Uniform Velocity / Uniform Acceleration – Straight line graph
Non-Uniform Velocity / Non-Uniform Acceleration – Graph can have different shapes
3. Equations of Motion
The equations of motion represent the relationship between an object’s acceleration, velocity and distance covered if and only if,
The object is moving on a straight path
The object has a uniform acceleration
Three Equations of Motion
1. The Equation for Velocity – Time Relation v = u + at
2. The Equation for Position – Time Relation s = ut + 1/2 at2
3. The Equation for the Position – Velocity Relation 2a s = v2 – u2 Where, u: initial velocity a: uniform acceleration t: time v: final velocity s: distance traveled in time t
Uniform Circular Motion
If an object moves in a constant velocity along a circular path, the change in velocity occurs due to the change in direction. Therefore, this is an accelerated motion.
Consider the figure given below and observe how directions of an object vary at different locations on a circular path.
When an object travels in a circular path at a uniform speed the object is said to have a uniform circular motion.
Non-Uniform Circular Motion
When an object travels in a circular path at a non-uniform speed the object is said to have a non-uniform circular motion
Examples of uniform circular motion:
The motion of a satellite in its or
The motion of planets around the sun
Velocity of Uniform Circular Motion Velocity = Distance/ Time = Circumference of circle / Time v = 2πr/ t where, v: velocity of the object r: radius of the circular path t: time taken by the object
Force
A force is an effort that changes the state of an object at rest or at motion. It can change an object’s direction and velocity. Force can also change the shape of an object.
Balanced force
When balanced forces are applied to an object, there will be no net effective force acting on the object. Balanced forces do not cause a change in motion.
Unbalanced force
When Unbalanced forces acting on an object change its speed and/or direction of motion. It moves in the direction of the force with the highest magnitude.
Net force
When multiple forces act on a body, they can be resolved into one component known as the net force acting on the object. For Example:
Friction
The force that opposes relative motion is called friction. It arises between the surfaces in contact. Example: When we try to push a table and it does not move is because it is balanced by the frictional force.
First Law of Motion or the law of inertia
A body continues to be in the state of rest or uniform motion in a straight line unless acted upon by an external unbalanced force. The First Law is also called the Law of Inertia.
Inertia
Basically, all objects have a tendency to resist the change in the state of motion or rest. This tendency is called inertia. All bodies do not have the same inertia.
Inertia depends on the mass of a body. Mass of an object is the measure of its inertia. More the mass more inertia and vice versa.
Inertia and Mass
The inertia of an object is dependent upon its mass.
Lighter objects have less inertia, that is, they can easily change their state of rest or motion.
Heavier objects have large inertia and therefore they show more resistance.
Hence ‘Mass’ is called a measure of the inertia of an object.
Momentum
Impacts produced by objects depend on their mass and velocity. The momentum of an object is defined as the product of its mass and velocity. p = mv. Vector quantity, has direction and magnitude.
Second Law of Motion
The rate of change of momentum of an object is directly proportional to the applied unbalanced force in the direction of the force. ⇒Δp/t α ma ⇒F α ma ⇒F = kma For 1 unit of force on 1 kg mass with the acceleration of 1m/s2, the value of k = 1. Therefore, F = ma.
Concept of system
The part of the universe chosen for analysis is called a system.
Everything outside the system is called an environment.
For example, a car moving with constant velocity can be considered a system. All the forces within the car are internal forces and all forces acting on the car from the environment are external forces like friction.
Conservation of momentum
The total momentum of an isolated system is conserved.
Isolated system net external force on the system is zero.
Example: Collision of 2 balls A and B.
mAUA+mBUB=mAVA+mBVB
Third Law of Motion
Newton’s 3rd law states that every action has an equal and opposite reaction. Action and reaction forces are equal, opposite and acting on different bodies.
Write the answer of the following questions.
What is the ultimate outcome when balanced forces act upon an object? a) The object remains stationary. b) The object accelerates. c) The object decelerates. d) The object moves at a constant velocity.
According to the fundamental law of motion, an object persists in its state of rest or uniform motion unless influenced by what? a) Unbalanced forces. b) Balanced forces. c) Frictional forces. d) Gravitational forces.
Inertia embodies the resistance of an object to alterations in which of the following? a) Direction. b) Velocity. c) Acceleration. d) All the mentioned.
As per the second law of motion, what parameter is directly linked to the acceleration of an object? a) Its mass. b) Its inertia. c) The applied force. d) None of the above.
What is the precise mathematical expression representing the second law of motion? a) F = m × a. b) F = m / a. c) F = m + a. d) F = m – a.
The third law of motion stipulates that for every action, there exists an equal and opposite reaction. What does this axiom entail? a) The reaction force is always equal in magnitude. b) The action and reaction forces act on different objects. c) The reaction force always acts in the opposite direction. d) All the mentioned.
If a person exerts a force of 500 N against a wall, what is the corresponding reaction force applied by the wall? a) 500 N. b) 0 N. c) It depends on the mass of the wall. d) None of the above.
Which among the subsequent scenarios exemplifies an unbalanced force? a) A book resting on a table. b) A car moving at a constant speed on a straight road. c) A ball falling freely towards the ground. d) A person exerting force to move a heavy box.
Which of the following scenarios best illustrates Newton’s first law of motion? a) A ball rolling down a hill. b) A book sliding on a table coming to a stop. c) A person riding a bicycle at a steady pace. d) A car accelerating after being at rest.
When a force of 10 N is applied to an object weighing 2 kg, what would be the resultant acceleration of the object? a) 20 m/s^2. b) 5 m/s^2. c) 2 m/s^2. d) 0.2 m/s^2.
Which of the following is an example of Newton’s third law of motion? a) A rocket launching into space b) A car accelerating on a straight road c) A person pushing a box across the floor d) A book resting on a table
When a person jumps from a boat to the shore, the boat moves backward due to: a) Action-reaction force b) Gravitational force c) Frictional force d) Buoyant force
An object of mass 10 kg is subjected to a force of 20 N. What is the acceleration of the object? a) 0.5 m/s² b) 2 m/s² c) 200 m/s² d) 10 m/s²
Which of the following is a unit of force in the SI system? a) Kilogram b) Meter per second c) Newton d) Pascal
A force of 50 N is applied to an object of mass 10 kg. What is the net force acting on the object if it is moving with a constant velocity? a) 5 N b) 10 N c) 50 N d) 0 N
When a car accelerates on a straight road, the force responsible for its acceleration is primarily due to: a) Frictional force b) Gravitational force c) Applied force d) Normal force
According to Newton’s second law of motion, the acceleration of an object is directly proportional to the: a) Net force acting on the object b) Mass of the object c) Velocity of the object d) Weight of the object
Which of the following is an example of inertia? a) A ball rolling down a hill b) A car turning around a curve c) A book at rest on a table remaining stationary d) A person pushing a heavy box
If the mass of an object is doubled while the force acting on it remains constant, what happens to its acceleration? a) It doubles b) It remains the same c) It halves d) It quadruples
Which of Newton’s laws states that an object will remain at rest or in uniform motion unless acted upon by an external force? a) Newton’s First Law b) Newton’s Second Law c) Newton’s Third Law d) Law of Gravitation