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Unit-3

Unit-3. Science. Unit 3.1 b. Lecture # 1 Unit 3.1 b. Contents: Fundamental and Derived units Table 1.  SI base units Table 2.  Examples of SI Derived units Prefixes of the SI system Volume, Area & Length Difference between Area & Volume

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Unit-3

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  1. Unit-3

  2. Science Unit 3.1 b

  3. Lecture # 1 Unit 3.1 b • Contents: • Fundamental and Derived units • Table 1.  SI base units • Table 2.  Examples of SI Derived units • Prefixes of the SI system • Volume, Area & Length • Difference between Area & Volume • Practice of L, A & V

  4. 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. Fundamental and Derived units

  5. 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.

  6. Differencebetween 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).

  7. PRACTICE OF L, A & V

  8. Science Unit 3.2 b

  9. Lecture # 2 Unit 3.2 b • Contents: • Mass • Force • Moment • Equilibrium • Static equilibrium • Relationship between mass, force & acceleration • Vectors • Resultant of two Coplanar forces • Head & tail Rule

  10. 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 field According 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). Mass

  11. 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.

  12. 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).

  13. 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.

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

  15. 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/m Which can e written as a = K.F/m Where 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/m Or F = m a The SI unit of force is the Newton ( N = kg-m/sec2) and it is denoted by N.

  16. 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.

  17. 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.

  18. Head & tail Rule

  19. Lecture # 3 Unit 3.2 b • Contents: • Examples of Force • Moment or torque formula • Examples of torque • Force and torque • Forces about a point • Simple Beams • Types of beams

  20. 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.

  21. 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: where τ 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.

  22. 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?

  23. How are force and torque related? moment arm A force can create a torque by acting through a moment arm. Force and Torque …produces a torque here. A force here... The relationship is t = F x r. r is the length of the moment arm (in this case, the length of the wrench).

  24. 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. Forces about a point • 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.

  25. 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.

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

  27. Science Unit 3.3 b

  28. Lecture # 4 Unit 3.3 b • Contents: • Displacement & Displacement • Example of Distance & Displacement • Speed • Examples of Speed • Velocity • Examples of Velocity • Acceleration • Examples of Acceleration • Vectors • Scalars

  29. 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.

  30. 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

  31. 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

  32. 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?

  33. 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

  34. 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#2If 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?

  35. 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 Acceleration

  36. Examples of Acceleration 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? 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? As we know F = m x a or F / m = a A = 20 N / 40 kg Acceleration =a = 0.5 m / s2

  37. 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

  38. 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.

  39. Lecture # 5 Unit 3.3 b • Contents: • 1st Equation Of Linear Motion For Constant Linear Acceleration • Example of Equation # 1 • 2nd Equation of Linear Motion for Constant Linear Acceleration • Example Of Equation # 2 • 3rd Equation of Linear Motion for Constant Linear Acceleration • Example of Equation # 3 • Distance, Time graph • Velocity, Time graph

  40. 1stEquation 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 / time For uniform accelerated motion average acceleration is equal to uniform acceleration Therefore 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.

  41. 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.

  42. 2ndEquation Of Linear Motion For Constant Linear Acceleration Suppose a body starts with an initial velocity viand 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 )/ 2 Also the total distance covered by the body S = Vav x t Substituting the value of Vav , we get = (vi + vf ) x t / 2 eq#3 Since vf = vi + at Therefore S = (vi + vi + at) x t / 2 Or S = vit + ½ at2 eq#4 Equation#4 establishes the relationship between distance, initial velocity, acceleration and time.

  43. 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.

  44. 3rdEquation 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

  45. 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.

  46. Distance Time graph

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