Unit-3

Unit-3

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Science

Unit 3.1 b

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Lecture # 1 Unit 3.1 b

• Contents:1. Fundamental and Derived units2. Table 1. SI base units 3. Table 2. Examples of SI Derived units4. Prefixes of the SI system5. Volume, Area & Length6. Difference between Area & Volume7. Practice of L, A & V

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Fundamental and Derived units

FUNDAMENTAL UNITS: Seven well-defined, dimensionally independent, fundamental units (or base units) that are assumed irreducible by convention.(meter, kilogram, second, ampere, Kelvin, mole, and candela).

DERIVED UNITS:A large number of derived units formed by combining fundamental units according to the algebraic relations of the corresponding quantities.

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Table 1. SI base units

BASE QUANTITY SYMBOL FOR QUANTITY NAME SYMBOL

Length l

meter m

Mass m

kilogram kg

Time t

second s

Electric current I

ampere A

Thermodynamic temperature T

Kelvin K

Amount of substance n

mole mol

Luminous intensity lʋ candela cd

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Table 2. Examples of SI derived units

DERIVED QUANTITY NAME SYMBOL

Area square meter m2

Volume cubic meter m3

Speed meter per second m/s

Velocity meter per second m/s

Acceleration meter per second squared m/s2

Force newton N

Pressure Pascal OR newton per meter squared Pa or N/m2

Torque newton meter N-m

Work joule OR newton meter J or N-m

Energy joule OR newton meter J or N-m

Power Watt OR joule per second W or J/s

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Prefixes of the SI system

PREFIX FACTOR SYMBOL

mega106

M

kilo103

k

milli 10−3 m

micro 10−6 µ

nano 10−9 n

pico 10−12 p

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• LENGTH• the linear extent in space from one end to the other; In geometric

measurements, length most commonly refers to the longest dimension of an object.

• The unit of length is “meter” (m) in SI system.

• AREA• Area is a quantity that expresses the extent of a two-dimensional surface or

shape in the plane.• A roughly bounded part of the space on a surface; a region.• The unit of area is “square meter (m2) in SI system.

• VOLUME• the amount of 3-dimensional space occupied by an object• Volume is how much three-dimensional space a substance (solid, liquid, gas,

or plasma) or shape occupies or contains.• The unit of volume is “cubic meter (m3) in SI system.

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Difference between Area & Volume

• Length is a measure of one dimension, whereas area is a measure of two dimensions (length squared) and volume is a measure of three dimensions (length cubed).

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PRACTICE OF L, A & V

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Science

Unit 3.2 b

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• Contents:1. Mass2. Force3. Moment4. Equilibrium5. Static equilibrium6. Relationship between mass, force & acceleration7. Vectors8. Resultant of two Coplanar forces9. Head & tail Rule

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Mass

The quantity of matter in a given body is the mass of the body and it can be measured from the equation.

m= F/a

The property of a body that causes it to have weight in a gravitational fieldAccording to Newton's second law of motion, if a body of fixed mass m is subjected to a force F, its acceleration a is given by F/m.

The SI unit of mass is the kilogram (kg).

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Force• Force is an agent which changes or tends to change the state of

rest or the motion of a body.• In physics, a force is any influence that causes a free body to

undergo a change in speed, a change in direction, or a change in shape.

• Force is a vector. The SI unit for force is the Newton (N). One Newton of force is equal to 1 kg * m/s2.

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Moment

• Moment of force (often just moment) is the tendency of a force to twist or rotate an object.

• The turning effect of a force is called torque or moment of the force. Moment of a force or torque may rotate an object in clock-wise or anti-clock-wise direction.

τ =f.r• The unit of Torque in SI units is Newton meter(N-m).

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Equilibrium• The state of a body or physical system at rest or in un

accelerated motion in which the resultant of all forces acting on it is zero and the sum of all torques about any axis is zero.

• A state of equal balance between weights, forces etc.• Two conditions for equilibrium are that the net force acting on

the object is zero, and the net torque acting on the object is zero.

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Static equilibrium• Any system in which the sum of the forces, and torque, on each

particle of the system is zero; mechanical equilibrium.• According to Newton’s second law of motion, we know that if the

net force acting on an object is zero the object has zero acceleration. If an object that is at rest or moves with a uniform velocity then the equilibrium is defined as “an object is in equilibrium when the object has zero acceleration.”

ΣFX = oΣFy= o

• This is the 2=1st condition of equilibrium.

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Relationship between mass, force & acceleration• According to Newton's Second Law, an object will move with constant

velocity until a force is exerted on the object. Or from a different angle, force effects acceleration.

• The acceleration produced by a particular force acting on a body is directly proportional to the magnitude of the force and inversely proportional to the mass of the body.

• The relationship between the force applied and the acceleration produced in an object can be mathematically expressed as

a α F (for a constant mass)

a α 1/m ( for a constant force)

i.e. a α F/mWhich can e written as a = K.F/mWhere K is a constant.In SI units F must have units of kilogram times meter per second squared if K has a value of 1.Therefore a = 1.F/mOr F = m a The SI unit of force is the Newton ( N = kg-m/sec2) and it is denoted by N.

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Vectors

• Physical quantities which require not only magnitude but also direction for their complete description. The directional quantities, are called vector quantities or simply vectors.

• e.g. Velocity, force, acceleration and momentum etc.

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Resultant of two Coplanar forces

To calculate the resultant of the force system shown above, move force A so that it's tail meets the head of force B. Now forces A and B form a "Head-to-Tail" arrangement. The resultant R is found by starting at the tail of B (the point of intersection of forces A and B) and drawing a vector which terminates at the head of the transposed A. Note that if force B had been transposed instead of force A, the resultant would have started from the tail of A and terminated at the head of force B. Again, this process could be repeated for any number of force vectors.

• The resultant is described by the vector's magnitude and direction. These are determined by scaling the length and angle respectively.

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Head & tail Rule

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• Contents:1. Examples of Force2. Moment or torque formula3. Examples of torque4. Force and torque5. Forces about a point6. Simple Beams7. Types of beams

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Examples of Force

Example#1: (Resultant of two forces)A boy walks 10m towards west, then 20m north and finally 20m east of north at an angle of 60°. Find the resultant displacement.

Example#2: (Resultant of 03 or more forces)A certain body is acted upon by forces of 30,60,40 and 70N. The direction of these forces make angles of 0°,60°,90° and 150° respectively with the x-axis. Find the resultant force acting on the body.Example#3: An object of mass 20 kg is moving with an acceleration of 3 m/s2. Find the force acting on it.

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Moment or Torque formula• Objects which can rotate about an axis will start rotating under the

action of a suitable force. The turning effect of a force is called torque or moment of the force.

• Moment of force or torque may rotate an object in clock-wise or anti-clock-wise direction.

• The symbol for torque is typically τ, the Greek letter tau. When it is called moment, it is commonly denoted M.

• The magnitude of torque depends on three quantities: First, the force applied; second, the length of the lever arm connecting the axis to the point of force application; and third, the angle between the two. In symbols:

whereτ is the torque vector and τ is the magnitude of the torque,r is the displacement vector (a vector from the point from which torque is measured to the point where force is applied), and r is the length (or magnitude) of the lever arm vector,F is the force vector, and F is the magnitude of the force,θ is the angle between the force vector and the lever arm vector.

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Example of Torque

• Example#1 : A force of 20N is applied at the edge of a wheel of radius 10cm. Find the torque acting on the wheel?

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Force and TorqueHow are force and torque related?

A force here...

…produces atorque here.

moment armA force can create a torque by acting through a moment arm.

The relationship is t = F x r. r is the length of the moment arm (in this case, the length of the wrench).

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Forces about a point

if all the forces are added together as vectors, then the resultant force (the vector sum) should be 0 Newton. (Recall that the net force is "the vector sum of all the forces" or the resultant of adding all the individual forces head-to-tail.) Thus, an accurately drawn vector addition diagram can be constructed to determine the resultant. Sample data for such a lab are shown below.

The resultant was 0 Newton (or at least very close to 0 N). This is what we expected - since the object was at equilibrium, the net force (vector sum of all the forces) should be 0 N.

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Simple Beams

A beam is generally considered to be any member subjected to principally to transverse gravity or vertical loading.The term transverse loading is taken to include end moments.There are many types of beams that are classified according to their size, manner in which they are supported, and their location in any given structural system.

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Types of beams

Types of Beams Based on the Manner in Which They are Supported.

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Science

Unit 3.3 b

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• Contents:1. Displacement & Displacement2. Example of Distance & Displacement3. Speed4. Examples of Speed5. Velocity6. Examples of Velocity7. Acceleration8. Examples of Acceleration9. Vectors10. Scalars

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Displacement & Distance

• Suppose a body is initially at position A. Let it move to position D. There may be various Paths along which we can move the body from A to D. This is called distance.

• But the directed distance form A to D is called displacement AD.

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Example of Distance & Displacement

• A body travels from A to D along a rectangular path ABCD. Find the total distance covered and its displacement.

AB = CD = 1m BC = 3m

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SPEED

• Speed is a distance covered per unit time. It is scalar. The direction does not matter. If you are on the highway whether traveling 100 km/h south or 100 km/h north, your speed is still 100 km/h.

• Speed(V) = total distance (S) covered/total time (t).

V = S/t

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Example of Speed

• Example : You drive a car for 2.0 h at 40 km/h, then for another 2.0 h at 60 km/h. What is your average speed?

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Velocity

• Velocity is a vector. Both direction and quantity must be stated. It one train has a velocity of 100km/h north, and a second train has a velocity of 100km/h south, the two trains have different velocities, even though their speed is the same.

• Average velocity = displacement / time.

V = S/t

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Example of velocity

• Example# 1 if a person walked 400 m in a straight line in 5 min, that person's velocity would be (400 m [forward])÷(5 min) = 80 m/min [forward] .

Example#2 If the same person walked 100 m [North] then 300 m [South] in 5 minutes, we first find their displacement.

displacement = 200 m [S]velocity = 200÷5 = 40 m/min [S]

Example#3• If that person walked 100 m [E] in .75 min, 100 m [N] in 1.50 min,

100 m [W] in 1.00 min and finally 100 m [S] in 1.75 min, find its velocity?

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Acceleration

Acceleration is a vector when it refers to the rate of change of velocity. Acceleration is scalar when it refers to rate of change of speed. A car slowing down to stop at a stop sign is accelerating because its speed is changing. We might refer to this type of acceleration as deceleration or negative acceleration. A car going at a constant speed around a curve is still accelerating because its direction is changing.acceleration = (change in velocity) ÷ time.

a = (vf - vi)/t

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Examples of Acceleration

Example#2 : A pitcher delivers a fast ball with a velocity of 43 m/s to the south. The batter hits the ball and gives it a velocity of 51m/s to the north. What was the average acceleration of the ball during the 1.0ms when it was in contact with the bat?

Example#1 : A box with a mass of 40 kg sits at rest on a frictionless tile floor. With your foot, you apply a 20 N force in a horizontal direction. What is the acceleration of the box?

As we know

F = m x a or

F / m = a

A = 20 N / 40 kg

Acceleration = a = 0.5 m / s2

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Vectors

• Physical quantities which require not only magnitude but also direction for their complete description. The directional quantities, are called vector quantities or simply vectors.

• e.g. Velocity, force, acceleration and momentum etc.

Force

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Scalars

Those quantities which are completely specified by their magnitude expressed in suitable units. They do no require any mention of direction for their representation. Scalars are added, subtracted, multiplied and divided according to ordinary arithmetical rules.

• e.g. volume, mass, length, speed, time, work and density etc.

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• Contents:1. 1st Equation Of Linear Motion For Constant Linear Acceleration2. Example of Equation # 13. 2nd Equation of Linear Motion for Constant Linear Acceleration4. Example Of Equation # 25. 3rd Equation of Linear Motion for Constant Linear Acceleration6. Example of Equation # 37. Distance, Time graph8. Velocity, Time graph

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1st Equation Of Linear Motion For Constant Linear Acceleration

• If an object is moving with uniform acceleration a and its velocity changes from initial velocity vi to final velocity vt in time interval t, then change in velocity,

Δv = vf - vi Average acceleration = change in velocity / timeFor uniform accelerated motion average acceleration is equal to uniform accelerationTherefore a = Δv / t =(vf – vi ) / t eq#1

a = (vf - vi )/ t or at = vf - vi vf = vi + at eq#2

This is the relationship between a, t, vi, and vf if any three of these are known then we can calculate the fourth one.

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EXAMPLE OF EQUATION # 1

Example: A motor car is moving with a uniform acceleration and attains the velocity of 36 km/h in 2 minutes. Find the acceleration of the car.

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2nd Equation Of Linear Motion For Constant Linear Acceleration

Suppose a body starts with an initial velocity vi and moves for t seconds with an acceleration a so that its final velocity becomes vf . We can find the distance covered by it as follows:The average velocity is given by the relation.

Vav = (vi + vf )/ 2Also the total distance covered by the body

S = Vav x tSubstituting the value of Vav , we get

= (vi + vf ) x t / 2 eq#3Since vf = vi + atTherefore S = (vi + vi + at) x t / 2 Or S = vit + ½ at2 eq#4Equation#4 establishes the relationship between distance, initial velocity, acceleration and time.

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Example Of Equation # 2

• Example: A car is moving with a velocity of 72 km/h. When brakes are applied it comes to rest after three seconds. Find the distance travelled by it before coming to rest.

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3rd Equation Of Linear Motion For Constant Linear Acceleration

The third equation of motion is relating, the initial velocity, the final velocity, the acceleration and the distance travelled. It can be obtained by eliminating t from the equation.

vf = vi + at Therefore t = (vf – vi ) / a

By substituting the value of t in eq#3, we have, s = (vi + vf )/ 2 + (vf – vi ) / a 2as = vf

2 - vi2 eq#5

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Example Of Equation # 3

• Example: A motorcyclist is moving with velocity of 72 km/h on a straight road. After applying brakes it comes to rest after covering a distance of 10m. Calculate its acceleration.

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Distance Time graph

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Velocity Time graph

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Science

Unit 3.4 b

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• Contents:1. Work2. Examples of work3. Energy4. Examples of Energy5. Power6. Examples of Power7. Law of Conservation of energy

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Work• When a force acts upon an object to cause a displacement of the

object, it is said that work was done upon the object. There are three key ingredients to work - force, displacement, and cause. In order for a force to qualify as having done work on an object, there must be a displacement and the force must cause the displacement.

• Mathematically, work can be expressed by the following equation.

The Joule is the unit of work.1 Joule = 1 Newton * 1 meter1 J = 1 N * m

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WORK cont.• Scenario A: A force acts rightward upon

an object as it is displaced rightward. In such an instance, the force vector and the displacement vector are in the same direction. Thus, the angle between F and d is 0 degrees.

• Scenario B: A force acts leftward upon an object that is displaced rightward. In such an instance, the force vector and the displacement vector are in the opposite direction. Thus, the angle between F and d is 180 degrees.

• Scenario C: A force acts upward on an object as it is displaced rightward. In such an instance, the force vector and the displacement vector are at right angles to each other. Thus, the angle between F and d is 90 degrees.

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Work cont.

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Example of work

• Example#1Find the work done when a force of 400N acting at an angle of 60° with the ground, moves an object 10m along the ground.

• Exmaple#2 Waiter who carried a tray full of meals above his head by one arm straight across the room at constant speed. Find the work done.

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Energy

Any body which can do work is said to posses energy.Energy may be defined as the capability of doing work. Energy can take a wide variety of forms.Thus, energy and work are measured in the same units i.e.. joules,but in many fields other units, such as kilowatt-hours and kilocalories, are customary.

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Example of energy

• A boy pushes a 5.00 kg cart in a circle, starting at 0.500 m/s and accelerating to 3.00 m/s. How much work was done on the cart?

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Power

• The rate at which work is performed or energy is converted.• The quantity work has to do with a force causing a displacement.• The standard metric unit of power is the Watt (joules/second).

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Examples of power

• Example#1 :When doing a chin-up, a physics student lifts her 42.0-kg body a distance of 0.25 meters in 2 seconds. What is the power delivered by the student's biceps?

• Example#2 : An escalator is used to move 20 passengers every minute from

the first floor of a department store to the second. The second floor is located 5.20 meters above the first floor. The average passenger's mass is 54.9 kg. Determine the power requirement of the escalator in order to move this number of passengers in this amount of time.

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Law of conservation of energy

• Within an isolated system, one type of energy can be transformed into another type of energy, but the total of all energies in the system is constant. The energy of a system changes by the work done on or by the system and the heat that enters or leaves the system.

• Energy can be neither created nor destroyed by ordinary means.• The five main forms of energy are:

– Heat– Chemical– Electromagnetic– Nuclear– Mechanical

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• Contents:1. Potential Energy2. Example of Potential Energy3. Kinetic Energy4. Examples of Kinetic Energy5. Distance, Time graph

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Potential energy

• Stored energy of position is referred to as potential energy. Potential energy is the stored energy of position possessed by an object.

• potential energy is the energy stored in a body or in a system due to its position in a force field or due to its configuration. The SI unit of measure for energy and work is the Joule (symbol J).

• PE = mass x g x height• PE = m x g x h

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Example of Potential Energy

• Example #1: Consider a body of mass 2kg placed on a table 1m high, which is placed on a platform of height 2m. Find potential energy of the body with respect to platform, and ground.

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Kinetic Energy

• Kinetic energy is the energy of motion. An object that has motion - whether it is vertical or horizontal motion - has kinetic energy. There are many forms of kinetic energy - vibrational (the energy due to vibrational motion), rotational (the energy due to rotational motion), and translational (the energy due to motion from one location to another).

• Work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes. The same amount of work is

done by the body in decelerating from its currentspeed to a state of rest.

where m = mass of object v = speed of object

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Example of Kinetic Energy

• Example #1: What is the kinetic energy of a body having mass 5 kg moving at a speed of 2 m/s.

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Kinetic energy cont.

• The faster an object moves, the more kinetic energy it has.• The greater the mass of a moving object, the more kinetic energy

it has.• Kinetic energy depends on both mass and velocity.

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Force Distance graph

Unit-3

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