Laws of motion

Made by:1) Rivan Patel2) Soham Sevak3) Jay Shah4) Abhishek Patel5) Kavin Shah

Chapter overview1) Force 9) Conservation of Momentum 2) Linear Momentum 10) Circular Motion 3) First law of Motion 11) Equilibrium of Concurrent4) Inertia Forces5) Second law of Motion 12) Solving Problems in 6) Impulse and its applications Mechanics 7) Third Law of Motion8) Friction and it’s types

Force

Force is an external effort in the form of push or pull, which :1) Produces or tries to produce motion in a body at rest.2) Stops or tries to stop a moving body.3) Changes the direction of motion of the body. It can be contact or non-contact as well as balanced or unbalanced force.

Linear momentum It is product of the mass and the velocity of the

body. Mathematically: :

It is a vector quantity. It’s SI Unit is kg ms-1. It’s dimensional formula is [M1L1T-1]. If two objects have a same linear momenta, then

the heavier will have smaller magnitude of velocity and the lighter object will have bigger magnitude of velocity.

Newton’s 3 Laws of Motion

First law of motionA body continues to be in its state of rest or of uniform motion along a straight line, unless it is acted upon by some net unbalanced external force to change the state.

If the net external force on a body is zero, its acceleration is zero. Acceleration can be non-zero only if there is a net external force on the body.

Inertia The inability of a body to change by itself its state of rest or state of uniform motion along straight line is called inertia of the body.

Newton’s first law defines inertia and is rightly called the law of inertia.

Quantitatively, inertia of a body in linear motion is measured by the mass of the body. Heavier the body, greater is the force required to change its state and hence greater is the inertia.

Three types of inertia(1) Inertia of RestIt is the ability of a body to change by itself, its state of rest.This rather means a body at rest remains at rest and cannot start moving on its own. When a person is standing in a stationary bus and the

driver starts the bus suddenly, he gets thrown backwards with a jerk due to inertia of rest.

The dust particles in a durree fall off when beaten with a stick. This is because the beating sets the durree in motion whereas the dust particles tend to remain at rest.

When we shake a branch of a mango tree, he mangoes fall down because branch comes in motion but mangoes tend to stay at rest.

Three types of inertia(2) Inertia of Motion It is the inability of body to change by itself, its state of uniform i.e. a body in uniform motion can neither accelerate nor retard on its own and come to rest. When a person is standing in a moving bus, and the driver

stops suddenly, he gets thrown forward with a jerk due to inertia of motion.

A person jumping out of a speeding train may fall forward. This is because his feet comes to rest on touching the ground and the remaining body continues to move due to inertia of motion.

An athlete runs a certain distance before taking a long jump. This is because velocity acquired by running is added to the velocity of the athlete at the time of jump.

Three types of inertia(3) Inertia of DirectionIt is inability of a body to change by itself, its direction of motion i.e. a body continues to move along the same straight line unless compelled by some external force to change it. The rotating wheels of any vehicle throw out mud,

tangentially, due to inertia of directional inertia.The Mud guards over the wheels stop this mud, protecting the clothes of the driver of the bike. When a knife is sharpened by pressing it against a

grinding stone, the sparks fly off along the tangent to the grinding stone, on account of directional inertia.

second law of motionThe rate of change of linear momentum of a body is directly proportional to the external force applied on the body, and this change takes place always in the direction of the applied force.

It is also called the real law of motion as both the other two laws are contained in it.

Dimensions of force: [M1L1T-2]. It is represented by Newton(N). It is a vector quantity.

1 Newton force is that much force which produces an acceleration of 1ms-2 in a body of mass 1 kg.

1 dyne is that force which produces an acceleration of 1 cm s-1 in a body of mass 1 gram.

1 kilogram weight is that much force which produces an acceleration of 9.8 ms-1 in a body of mass 1 kg.

impulseImpulse of a force is a measure of total effect of the force. Impulse= average force X time It is measured by the total change in linear momentum

produced during the impact. The forces which act on bodies for short time are called

impulsive forces. Eg. Jumping, kicking, catching, etc. According to impulse-momentum, the linear momentum

can be produced by applying a larger force for a shorter time or by applying a smaller force for a longer time.

F1 X t1 = F2 X t2

Application of the concept of impulse

A cricket player lowers his hands while a cricket ball. This takes more time for

ball to reach the ground, thus reducing the impact of ball on his hands. China wares and glasswares are wrapped in paper or straw pieces while

packing. In the event of fall, impact will take a longer time to reach the articles through paper/straw. As a result, the average force exerted on the articles is small and chances of their breaking reduce.

An athlete is advised to come to stop slowly, after finishing a fast race, so that time of stop increases and hence force experienced by him decreases.

It is difficult to catch a cricket ball than to catch a tennis ball. The cricket ball being heavier has a much larger momentum and therefore, exerts a much larger force on the hands during catch, in comparison to the force exerted by tennis ball.

Third law of motionTo every action, there is an equal and opposite reaction.

According to Newton, force never occurs singly in nature. Forces always occur in pairs as a result of mutual

interaction between two bodies

The third law tells us what is the origin of external force on the

on the body.

FAB = -FBA

Application of the concept of third law of motion

frictionForce that opposes the motion of an object when the object is in contact with another object or surface is called friction.We can classify friction into two types:1) External or dry friction, which arises when two bodies contact with each other try to move or there is an actual relative motion between the two. The external friction is also called contact friction.2) Internal friction, which arises on account of relative motion between every layers of a liquid. It is also referred to as viscosity of the liquid.

External friction Static friction The opposing force comes into play when one body tends

to move over the surface of another, but the actual motion has not yet started is called Static friction.

It opposes impending motion.Limiting friction Limiting friction is the maximum force that comes into

play, when one body is just at the verge of moving over the surface of the other body.

Coefficient of limiting friction between any two surfaces is defined as the ratio of the force of limiting friction and normal reaction between them.

Kinetic/Dynamic friction It is the opposing force that comes into play when one

body is actually moving over the surface of another body. Kinetic friction is always slightly less than the limiting

friction. It is of two types:1) Sliding friction-The opposing force that comes into play when one body is actually sliding over the surface of the other body is called sliding friction.2) Rolling friction-The opposing force that comes into play when one body is actually rolling over the surface of the other body is called rolling friction.

Laws of kinetic friction

1)The force of kinetic friction is directly proportional to normal reaction (R) between the two surfaces in contact.

2) Kinetic friction does not depend upon the surface area of contact.

3) Force of kinetic friction is independent of the speed of sliding/rolling, if the heat produced does not change the condition of the surfaces in contact.

Laws of limiting friction1) The magnitude of the force of limiting friction between the surfaces of two bodies in contact is directly proportional to the normal reaction between them. 2) Direction of the force of limiting friction is always opposite to the direction in which one body is at the verge of moving over the other.3) The force of limiting friction is independent of the apparent area of contact, so long as normal reaction between the two surfaces in contact remains the same.

angle of friction

The angle of friction between any two surfaces in contact is defined as the angle which the resultant of the force of limiting friction and normal reaction makes with the direction of normal reaction.Coefficient of limiting friction between any two surfaces in contact is equal to tangent of the angle of friction between them.

Importance of friction Walking is not possible without friction between our

poot and the ground. No two surfaces will stick to each other if there is no

friction. Brakes of vehicles will not work without friction. Writing on black board is not possible without

friction. Adhesives will lose their purpose. Friction between a match stick and the match box

causes the match stick to catch fire.

disadvantages of frictionDespite the fact that the friction is very important in our daily life, it also has some disadvantages like:1. The main disadvantage of friction is that it produces heat in various parts of machines. In this way some useful energy is wasted as heat energy.2. Due to friction we have to exert more power in machines.3. It opposes relative motion which causes loss of velocity. 4. More noise is produced in machines because of friction.5. Due to friction, engines of automobiles consume more fuel which is a money loss. 

Methods of reducing friction By polishing By lubrication By proper selection of materials By streamlining and reducing drag By using ball bearings

principal of Conservation of linear momentum

According to this principal, in an isolated system, the vector sum of the linear momenta of all the bodies in the system is conserved and is not affected due to their mutual action and reaction.

Total momentum before collision = Total momentum after collision

Change in linear momentum of the system is zero.

Total linear momentum of the system remains constant.

In the interaction between two bodies A and B, the force that A exerts on B is equal and opposite to the force that B exerts on A.

Consider a collision between two objects - object 1 and object 2. For such a collision, the forces acting between the two objects are equal in magnitude and opposite in direction (Newton's third law). This statement can be expressed in equation form as follows: F1 = -F2

Regardless of how long the time is, it can be said that the time that the force acts upon object 1 is equal to the time that the force acts upon object 2. This is merely logical i.e. t1 = t2

 It follows that the impulses experienced by the two objects are also equal in magnitude and opposite in direction. As an equation, this can be stated as F1*t1 = F2*t2

But the impulse experienced by an object is equal to the change in momentum of that object (the impulse-momentum change theorem). Thus they must experience equal and opposite momentum changes. i.e. m1*Δv1 = -m2*Δv2

For example:

uniform Circular motionA uniform circular motion is the motion of an object travelling at a constant (uniform) speed along a circular path.Centipetal forceIt is the force required to move a body uniformly in a circle. This force acts along the radius towards the centre of the circle. Centipetal force = mass X centripetal accelerationCentrifugal forceIt is a force that arises when a body is actually moving along a circular path, by virtue of tendency of the body to regain its natural straight line path.It acts along the radius and away from the centre of the circle.

Equilibrium of concurrent forcesThe forces which are acting at the same point are called concurrent forces.Equilibrium of a particle in mechanics refers to the situation when the net external force on the particle is zero i.e. when the particle has zero acceleration. According to Newton’s first law, this means that the particle would be either at rest or in uniform linear motion.

R= F1 + F2 + F3 = 0 Three concurrent forces F1, F2 and F3 will be in equilibrium, when resultant of F1 and F2 is equal and opposite to F3.

Equation of equilibriumIf we label the forces acting on the particle by A, B, C, ... , then the condition for the equilibrium of a particle may be written in the form of an equation as R = A + B + C + .… = 0 Where R is the resultant of the forces acting on the particle. We know that a vector equation may be resolved into three independent scalar equations, one for each of three mutually perpendicular directions, so that the equation may be written as: Rx = 0 = Ax + Bx + Cx Ry = 0 = A y + By + Cy Rz = 0 = A z + Bz + Cz

Solving problems in mechanicsTo solve typical problems in mechanics, we use the following steps:1) Draw a diagram showing various parts of the system with links, supports etc.2) Choose any one convenient part of the system.3) Draw a separate diagram of the chosen part showing all the forces on the chosen part by the remaining parts of the system. A diagram of this type is called free body diagram.4) In free body diagram, include information about magnitude and direction of forces that are either given or you are sure of.Equate the net force acting in a particular direction to its mass times acceleration produced in that direction.

Solving problems in mechanicsComponents of solving problems in mechanics:1) Time2) Displacement3) Velocity4) Acceleration5) Mass6) Graphs of above relations

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