1. AFE BABALOLA UNIVERSITY DEPARTMENT OF PHYSICAL SCIENCES

2. PHY 101 : MECHANICS

3. Course Outlines Measurement in Physics Space and Time Units and Dimension Kinematics Fundamental Laws of Mechanics Statics and Dynamics Work and Energy Conservation laws

4. “ If I have ever made any valuable discoveries, it has been owing more to patient attention, than to any other talent.” -Sir Isaac Newton

5. My First Day In Class What is my teacher’s Name? What is my Name? What do my teacher want from me? What is my teaher’s expectation from me?

6. Mechanics The subject of mechanics deals with the motion or the state of rest of a given material object, body or particle. Mechanics is divided into two parts: (i) Kinematics (ii) Dynamics However, Mechanics is the study of the effects of external forces on the bodies at rest or in motion. Such bodies could be rigid or elastic solids, liquids or gases.

7. The quantitative concepts used in mechanics can be classified into two groups: 1.The fundamental concepts, consisting of length, mass and time 2.The derived concepts, such as density, area, speed, energy and power. Each quantity is measured by comparing it with a standard or unit.

8. Space and Time Space is the position at a distance from another. It is as well an item without a unit mass of substance. It is however an interval of time. The unit of time is seconds. This is the S.I unit. Thus, any time standard must be able to answer two questions: “When did it happen ?” “What is its duration ?”

9. Units and Dimensions Unit is defined as the measure that specify the magnitude of a particular quantity. In Physics “The International System of Units usually referred to as S I unit ” is the generally accepted standard or unit. For example the international system of units specifies the metre (m) as the unit of length, the kilogram (kg) as the unit of mass and the second (s) as the unit of time.

10. These are fundamental units. Units for other quantities such as density, area, speed, energy are derived units. Other fundamental quantities which are defined in other branches of physics are temperature and electric current. Dimension is the representation of system of units in symbols. However, dimension quantities are heritage of the combination of fundamental quantities represented in symbols.

11. Physical Quantities Physical quantity is defined as a quantity that can be measured. Examples of physical quantities are length, mass, time, weight, electric current, force, velocity, and momentum. When stating a physical quantity, two items are involved, namely thus, the numerical value and the unit. For example the height of a boy is 1.75m, the numerical value is 1.75 and the unit of the height is meter (m).

12. Basic Quantities and Base Units The basic quantities in Physics are the fundamental quantities which are assigned base units. The units for the basic physical quantities are known as base units. Physics involves many physical quantities of which seven are chosen as physical quantities in S.I Units.

13. Basic QuantitiesBase UnitsSymbols Lengthmeterm MassKilogramKg TimeSeconds Electric CurrentampereA TemperatureKelvinK Amount of Substance molemol Luminous Intensitycandelacd

14. Derived Quantities and Derived Units A derived Quantity is a combination of various basic quantities. Units for derived quantities are called derived units. However, the derived unit for a derived quantity can be obtained from the relationship between the derived quantity with the basic quantities. The following table shows example of derived quantities and their units.

15. Derived QuantitiesDerived Units Area m 2 Volume m 3 Density Kg m -3 Velocity m s -1 Acceleration m s -2 ForceN or Kg m s -2 PressurePa or Kg m -1 s -2 EnergyJ or Kg m 2 s -2 PowerW or Kg m 2 s -3 Electric Charge C or A s VoltageV or Kg m 2 s -3 A -1 Resistance Ω or V A -1

16. Summary: Mechanics is a subject of physics that deals with the motion or the state of rest of a given body. Mechanics is divided into two parts kinematics and dynamics. Unit is the measure that specify the magnitude of a particular quantity. Dimension is the representation of system of units in symbols. Physical quantity is a quantity that can be measured. Examples include length, mass, time, weight, electric current, force, velocity, and momentum.

17. In the last class contd. Basic quantities are the fundamental quantities which are assigned base units. A derived quantity is a combination of various basic quantities and is assigned derived unit.

18. USES OF DIMENSIONAL EQUATIONS 1.To check the homogeneity of a physical equation (i.e. to check the correctness of a physical equation). 2.To derive the unit of a Physical Quantity 3. To derive a relationship between different physical quantities. 4. To derive the exact form of a Physical Equation

19. “ If I have ever made any valuable discoveries, it has been owing more to patient attention, than to any other talent.” -Sir Isaac Newton

20. Uses of Units and Dimensions (i) To Check the homogeneity of Physical Equations Example 1 Check that : S = ut + ½ at 2 which relate that the displacement S, initial velocity u, time t, and acceleration a, in motion under uniform acceleration, is dimensionally homogeneous.

21. Solution

22. (2) To derive the unit of a Physical Quantity

23. Solution

25. (3) Deriving the exact form of a Physical Equation Determining a physical quantity usually depends on a number of other physical quantities. Example 3 The period T of a simple pendulum depends on its length l and the acceleration due to gravity g. Using units or dimensions, derive an equation to relate the period T with ‘l’ and ‘g’.

26. Solution T α (l) x (g) y (1) T = K (l) x (g) y (2) Note : where K, x, y are non dimensional constants Dimensionally, unit of Period T = s, dimension T (i) unit of length l = m, dimension L (ii) unit of g (acceleration) = ms -2, dimension LT -2 (iii)

27. Substituting (i) to (iii) into equation (2), we have, T = (L) x (LT -2 ) y T = (L ) x (L) y (T ) -2y T = L (x+y) (T ) -2y It’s possible, eqn (3) is written as, L 0 T 1 = L (x+y) T -2y x + y = 0 -2y = 1 from (1), x = ½ y = - ½

28. Substitution x and y values in eqn(2) above, T = k (l) ½ (g) -1/2 (*)(*) Equation (*) (*) gives the derived expression for the period T.

29. Class Exercise 1 Poiseuille assumed that the rate of flow of a liquid through a horizontal tube under streamline flow depends on : (a) a, radius of the tube (b) ŋ, viscosity of the liquid, and (c) р/l, the pressure gradient along the tube. where р = pressure difference across the length of the tube. l = length of the tube. Using Poiseuille’s assumption, derive an expression for the rate of flow of a liquid through a horizontal tube in terms of a, l, р and ŋ (Unit for Viscosity = kg m -1 s -1 )

30. Solution The rate of flow in a fluid is the Volume change per unit time, Thus we have, The rate of flow, = dV/dt :. dV/dt = k (a) x (ŋ) y (р/l) z Where k,x,y,z are dimensionless constants. L 3 T -1 = L x (ML -1 T -1 ) y (M L -2 T -2 ) z =L x (M y L -y T -y ) (M z L -2z T -2z ) L 3 T -1 =L x-y-2z M y+z T -y-2z

31. x –y -2z =3 ………………(1) y + z =0 …………….... (2) -y -2z = -1 ……………..(3) From equation, (2) y = -z Therefore,from (3) z=1

32. Hence, y = -1 From eqn (1), substituting for ‘y’ and ‘ z’ x – (-1) -2(1) =3 x + 1 -2 =3 x-1 =3 x =3 +1 x =4

33. is the expression for the rate of flow of a liquid through a horizontal tube in terms of a, l, р and ŋ Therefore, dV /dt = Ka 4 p/ŋ l

34. Kinematics and Dynamics Basic Definitions Kinematics is the mathematical description of the motion of objects without any explanation of the cause of the motion. Dynamics on the other hand, relates the motion of objects to the causes of such motion. We shall begin our study with of mechanics with the kinematics of particles.

35. What is Motion? Motion is defined as the tendency of a body to change it state or position. The world and everything in it, moves. Even seemingly stationary things such as a roadway moves with Earth rotation.

36. General Properties of Motion 1.The motion is along a straight line. The line may be vertical, horizontal, or slanted, but it must be straight. 2.Force ( push or Pull ) cause motion. 3.The moving object is either a particle for example, an electron or an object that moves like an electron, for example a pig slipping down a straight playground. 4.

37. Position and Displacement Position means the location of an object relative to some reference point, often called the origin or zero point. For example, a particle might be located at x = 5m, which means it is 5m in the positive direction from the origin.If it were at x = -5m it would just be 5m from the origin in the opposite direction.

38. Motion in one dimension One dimensional motion is the motion of a particle in a straight line, from one point to another. It is also called rectilinear motion. In the kinematics of one dimensional motion, we ask the following questions: 1. What distance and in which direction? 2. what is its displacement? 3. How fast is it moving or what is its speed?

39. 4. Is it speeding up or slowing down or what is its acceleration? Displacement means a change from a position to another position, i.e a change from a position x 1 to position x 2 is called displacement. ∆ x =X 2 –X 1 …………..(1)

40. Motion Under Uniform Acceleration As earlier discussed, Kinematics is defined as the study of the motion of objects without referring to what causes the motion. Motion is a change in position in a time interval. However, to discuss motion under uniform acceleration, we will restrict ourselves to motion in a straight line. See below,

41. V O P The displacement ‘S’ of an object from a fixed point ‘O’ is the distance moved by P along straight line ‘OP’. Since displacement has both magnitude and direction, it is however a ‘vector quantity’.

42. Equation of uniformly accelerated motion

44. First Equation of Motion

45. Second Equation of Motion

47. (Reviews) What is constant Acceleration? State the First Equation for one dimensional Motion. State the Second Equation for one dimensional Motion. Differentiate between a Cartesian System and a co – ordinate system.

48. Third Equation of Motion