Laws of Motion Online Test 10th Science Lesson 1 Questions in English

Things around us are related to one another. Some bodies are at rest and some are in motion. Rest and motion are interrelated terms. There are various types of motion such as linear motion, circular motion, oscillatory motion, and so on.

Let us define force in a more scientific manner using the three laws proposed by Sir Isaac Newton. These laws help you to understand the motion of a body and also to predict the future course of its motion, if you know the forces acting on it. Before Newton formulated his three laws of motion, a different perception about the force and motion of bodies prevailed.

Kinetics deals with the motion of bodies considering the cause of motion. Kinematics deals with the motion of bodies without considering the cause of motion.

Statics deals with the bodies, which are at rest under the action of forces. Dynamics is the study of moving bodies under the action of forces. Dynamics is further divided into Kinematics and Kinetics.

According to Aristotle a Greek Philosopher and Scientist, the natural state of earthly bodies is ‘rest’. He stated that a moving body naturally comes to rest without any external influence of the force. Such motions are termed as ‘natural motion’ (Force independent).

Aristotle proposed that a force (a push or a pull) is needed to make the bodies to move from their natural state (rest) and behave contrary to their own natural state called as ‘violent motion’ (Force dependent). Further, he said, when two different mass bodies are dropped from a height, the heavier body falls faster than the lighter one.

Galileo proposed the following concepts about force, motion and inertia of bodies: • Th e natural state of all earthly bodies is either the state of rest or the state of uniform motion. • A body in motion will continue to be in the same state of motion as long as no external force is applied. • When dropped from a height in vacuum, bodies of different size, shape and mass fall at the same rate and reach the ground at the same time.

While you are travelling in a bus or in a car, when a sudden brake is applied, the upper part of your body leans in the forward direction. Similarly, when the vehicle suddenly is move forward from rest, you lean backward. This is due to, anybody would like to continue to be in its state of rest or the state of motion. This is known as ‘inertia’. The inherent property of a body to resist any change in its state of rest or the state of uniform motion, unless it is influenced upon by an external unbalanced force, is known as ‘inertia’.

There are three types of inertia. They are Inertia of rest, Inertia of motion, Inertia of direction. a) Inertia of rest: The resistance of a body to change its state of rest is called inertia of rest. b) Inertia of motion: The resistance of a body to change its state of motion is called inertia of motion. c) Inertia of direction: The resistance of a body to change its direction of motion is called inertia of direction

In activity described above, the inertia of the coin keeps it in the state of rest when the cardboard moves. Then, when the cardboard has moved, the coin falls into the tumbler due to gravity. This happens due to ‘inertia of rest’.

• An athlete runs some distance before jumping. Because, this will help him jump longer and higher. (Inertia of motion) • When you make a sharp turn while driving a car, you tend to lean sideways, (Inertia of direction). • When you vigorously shake the branches of a tree, some of the leaves and fruits are detached and they fall down, (Inertia of rest).

The impact of a force is more if the velocity and the mass of the body is more. To quantify the impact of a force exactly, a new physical quantity known as linear momentum is defined.

The product of mass and velocity of a moving body gives the magnitude of linear momentum. It acts in the direction of the velocity of the object. Linear Momentum = mass × velocity

Linear momentum is a vector quantity. It helps to measure the magnitude of a force. Unit of momentum in SI system is kg m s–1 and in C.G.S system its unit is g cm s-1.

Newton’s First Law states that every - body continues to be in its state of rest or the state of uniform motion along a straight line unless it is acted upon by some external force. It gives the definition of force as well as inertia.

Force is an external effort in the form of push or pull, which: 1. produces or tries to produce the motion of a static body. 2. stops or tries to stop a moving body. 3. changes or tries to change the direction of motion of a moving body. Force has both magnitude and direction. So, it is a vector quantity.

Based on the direction in which the forces act, they can be classified into two types as: (a) Like parallel forces and (b) Unlike parallel forces. • Like parallel forces: Two or more forces of equal or unequal magnitude acting along the same direction, parallel to each other are called like parallel forces. • Unlike parallel forces: If two or more equal forces or unequal forces act along opposite directions parallel to each other, then they are called unlike parallel forces.

When several forces act simultaneously on the same body, then the combined effect of the multiple forces can be represented by a single force, which is termed as ‘resultant force’. It is equal to the vector sum (adding the magnitude of the forces with their direction) of all the forces. If the resultant force of all the forces acting on a body is equal to zero, then the body will be in equilibrium. Such forces are called balanced forces. If the resultant force is not equal to zero, then it causes the motion of the body due to unbalanced forces. Examples: Drawing water from a well, force applied with a crow bar, forces on a weight balance, etc.

A system can be brought to equilibrium by applying another force, which is equal to the resultant force in magnitude, but opposite in direction. Such force is called as ‘Equilibrant’.

The door can be easily opened or closed when you apply the force at a point far away from the fixed edge. In this case, the effect of the force you apply is to turn the door about the fixed edge. This turning effect of the applied force is more when the distance between the fixed edge and the point of application of force is more.

The rotating or turning effect of a force about a fixed point or fixed axis is called moment of the force about that point or torque (τ).

Torque is measured by the product of the force (F) and the perpendicular distance (d) between the fixed point or the fixed axis and the line of action of the force. τ = F × d

Torque is a vector quantity. It is acting along the direction, perpendicular to the plane containing the line of action of force and the distance. Its SI unit is N m.

Two equal and unlike parallel forces applied simultaneously at two distinct points constitute a couple. The line of action of the two forces does not coincide. It does not produce any translatory motion since the resultant is zero. But, a couple results in causes the rotation of the body. Rotating effect of a couple is known as moment of a couple.

Moment of a couple is measured by the product of any one of the forces and the perpendicular distance between the line of action of two forces. The turning effect of a couple is measured by the magnitude of its moment. M = F × S The unit of moment of a couple is newton metre (N m) in SI system and dyne cm in CGS system.

By convention, the direction of moment of a force or couple is taken as positive if the body is rotated in the anti-clockwise direction and negative if it is rotate in the clockwise direction.

Application of Torque: • A gear is a circular wheel with teeth around its rim. It helps to change the speed of rotation of a wheel by changing the torque and helps to transmit power. • Most of you have played on the sea-saw. Since there is a difference in the weight of the persons sitting on it, the heavier person lifts the lighter person. When the heavier person comes closer to the pivot point (fulcrum) the distance of the line of action of the force decreases. It causes less amount of torque to act on it. This enables the lighter person to lift the heavier person. • A small steering wheel enables you to manoeuore a car easily by transferring a torque to the wheels with less effort.

When a number of like or unlike parallel forces act on a rigid body and the body is in equilibrium, then the algebraic sum of the moments in the clockwise direction is equal to the algebraic sum of the moments in the anticlockwise direction. In other words, at equilibrium, the algebraic sum of the moments of all the individual forces about any point is equal to zero.

According to Newton’s Second law, “the force acting on a body is directly proportional to the rate of change of linear momentum of the body and the change in momentum takes place in the direction of the force”. This law helps us to measure the amount of force. So, it is also called as ‘law of force’

Force is required to produce the acceleration of a body. In a uniform circular motion, even though the speed (magnitude of velocity) remains constant, the direction of the velocity changes at every point on the circular path. So, the acceleration is produced along the radius called as centripetal acceleration. The force, which produces this acceleration is called as centripetal force

Units of force: SI unit of force is newton (N) and in C.G.S system its unit is dyne. Definition of 1 newton (N): The amount of force required for a body of mass 1 kg produces an acceleration of 1 m s –2, 1 N = 1 kg m s –2.

The amount of force required for a body of mass 1 gram produces an acceleration of 1 cm s –2, 1 dyne = 1 g cm s -2; also 1 N = 10^5 dyne.

A large force acting for a very short interval of time is called as ‘Impulsive force’. When a force F acts on a body for a period of time t, then the product of force and time is known as ‘impulse’ represented by ‘J’ Impulse, J = F × t

Impulse, J = F × t By Newton’s second law F = Δ p / t (Δ refers to change), Δ p = F × t Impulse is also equal to the magnitude of change in momentum. Its unit is kg m s-1 or N s.

Newton’s third law states that ‘for every action, there is an equal and opposite reaction. They always act on two different bodies. If a body A applies a force FA on a body B, then the body B reacts with force FB on the body A, which is equal to FA in magnitude, but opposite in direction. Fb = –Fb.

Examples Newton’s third law of Motion: • When birds fly, they push the air downwards with their wings (Action) and the air pushes the bird upwards (Reaction). • When a person swims, he pushes the water using the hands backwards (Action), and the water pushes the swimmer in the forward direction (Reaction). • When you fire a bullet, the gun recoils backward and the bullet is moving forward (Action) and the gun equalises this forward action by moving backward (Reaction).

There is no change in the linear momentum of a system of bodies as long as no net external force acts on them. m1v1 + m2v2 = m1u1 + m2u2 The above equation confirms in the absence of an external force, the algebraic sum of the momentum after collision is numerically equal to the algebraic sum of the momentum before collision.

Propulsion of rockets is based on the law of conservation of linear momentum as well as Newton’s III law of motion.

Rockets are filled with a fuel (either liquid or solid) in the propellant tank. When the rocket is fired, this fuel is burnt and a hot gas is ejected with a high speed from the nozzle of the rocket, producing a huge momentum. To balance this momentum, an equal and opposite reaction force is produced in the combustion chamber, which makes the rocket project forward.

While in motion, the mass of the rocket gradually decreases, until the fuel is completely burnt out. Since, there is no net external force acting on it, the linear momentum of the system is conserved.

The mass of the rocket decreases with altitude, which results in the gradual increase in velocity of the rocket. At one stage, it reaches a velocity, which is sufficient to just escape from the gravitational pull of the Earth. This velocity is called escape velocity.

Newton’s universal law of gravitation states that every particle of matter in this universe attracts every other particle with a force. This force is directly proportional to the product of their masses and inversely proportional to the square of the distance between the centres of these masses. The direction of the force acts along the line joining the masses.

Force between the masses is always attractive and it does not depend on the medium where they are placed.

Let, m1 and m2 be the masses of two bodies A and B placed r metre apart in space, Force, F ∝ m1 × m2 F ∝ 1/ r2 F = G m1 m2/ r^2 Where G is the universal gravitational constant. Its value in SI unit is 6.674 × 10–11 N m^2 kg^–2.

The velocity of the object keeps changing as it falls down. This change in velocity must be due to the force acting on the object. The acceleration of the body is due to the Earth’s gravitational force. So, it is called as ‘acceleration due to the gravitational force of the Earth’ or ‘acceleration due to gravity of the Earth’. It is represented as ‘g’. Its unit is m s ^–2.

Mean value of the acceleration due to gravity is taken as 9.8 m s ^–2 on the surface of the Earth. This means that the velocity of a body during the downward free fall motion varies by 9.8 m s^–1 for every 1 second. However, the value of ‘g’ is not the same at all points on the surface of the earth.

The radius of the Earth is R =6378 km = 6400 km approximately. By Newton’s law of gravitation, the force acting on the body is given by, F = G M m/ R^2.

According to Newton’s second law of motion, the force acting on the body is given by the product of its mass and acceleration (called as weight). Here, acceleration of the body is under the action of gravity hence a = g. F = m a = m g Acceleration due to gravity g = GM / R^2

Mass of the Earth M = g R^2 /G Substituting the known values of g, R and G, you can calculate the mass of the Earth as M = 5.972 × 10^24 kg

Since, g depends on the geometric radius of the Earth, (g ∝ 1/R^2), its value changes from one place to another on the surface of the Earth. Since, the geometric radius of the Earth is maximum in the equatorial region and minimum in the polar region, the value of g is maximum in the polar region and minimum at the equatorial region.

When you move to a higher altitude from the surface of the Earth, the value of g reduces. In the same way, when you move deep below the surface of the Earth, the value of g reduces. Value of g is zero at the centre of the Earth.

Mass is the basic property of a body. Mass of a body is defined as the quantity of matter contained in the body. Its SI unit is kilogram (kg).

Weight is a vector quantity. Direction of weight is always towards the centre of the Earth. SI unit of weight is newton (N). Weight of a body varies from one place to another place on the Earth since it depends on the acceleration due to gravity of the Earth (g), which is not the same at all places on the Earth.

The value of acceleration due to gravity on the surface of the moon is 1.625 ms–2. This is about 0.1654 times the acceleration due to gravity of the Earth. If a person whose mass is 60 kg stands on the surface of Earth, his weight would be 588 N (W= mg = 60 × 9.8). If the same person goes to the surface of the Moon, he would weigh only 97.5 N (W = 60 × 1.625). But, his mass remains the same (60 kg) on both the Earth and the Moon.

The weight that you feel to possess is not the same as your actual weight called apparent weight. Apparent weight is the weight of the body acquired due to the action of gravity and other external forces acting on the body.

Some of us believe that the astronauts in the orbiting space station do not experience any gravitational force of the Earth. So, they float. But this is absolutely wrong. Astronauts are not floating but falling freely around the earth due to their huge orbital velocity. Since space station and astronauts have equal acceleration, they are under free fall condition. Hence, both the astronauts and the space station are in the state of weightlessness.

Application of Newton’s law of gravitation: 1) Dimensions of the heavenly bodies can be measured using the gravitation law. Mass of the Earth, radius of the Earth, acceleration due to gravity, etc. can be calculated with a higher accuracy. 2) Helps in discovering new stars and planets. 3) One of the irregularities in the motion of stars is called ‘Wobble’ leads to the disturbance in the motion of a planet nearby. In this condition the mass of the star can be calculated using the law of gravitation. 4) Helps to explain germination of roots is due to the property of geotropism which is the property of a root responding to the gravity. 5) Helps to predict the path of the astronomical bodies.