1. www.soran.edu.iq Muna salah al-deen General Physics 1

2. www.soran.edu.iq 2 week1 General Physics Contents A. Mechanics 1.Physics and measurement 2. Motion and dimensions 3. Vectors 4. Motion in two dimensions 5. Laws of motion 6. Circular motion 7. Energy 8. Potential energy 9. Linear momentum and collision 10. Rotation 11. Angular momentum B. Properties of Matter 12. Static and Elasticity 13. Universal gravitation 14. Fluid mechanics

3. www.soran.edu.iq 1.Physics and measurement 1.1 SI prefixes for power of ten 1.2 The Greek Alphabet 1.3 Standard Abbreviations and Symbols for Units 1.4 Mathematical Symbols and their meaning 1.5The Fundamental SI units 1.6 Dimensional Analysis 3

4. www.soran.edu.iq 4 1.5 The Fundamental SI units The Fundamental SI units quantityunitabbreviation Masskilogramkg Lengthmeterm Timeseconds TemperaturekilvinK Electric currentampereA Luminous intensitycandelacd Amount of substancemolemol

5. www.soran.edu.iq Motion in one dimension week2 5 2.1 Position, velocity, and speed 2.2 Instantaneous velocity and speed 2.3 Acceleration 2.4 One-Dimensional motion with constant acceleration 2.5 Freely Falling Objects

6. www.soran.edu.iq  The displacement of a particle is defined as its change in position in some time interval. ∆x = x f – x i …………. (2.1) Instantaneous velocity  The instantaneous velocity is v x equals the limiting value of the ratio ∆x / ∆t as ∆t approaches zero: v x = lim (∆x / ∆t) = dx /dt ……….. (2.4) ∆t---------0  The instantaneous velocity can be positive, negative, and zero. Instantaneous speed Instantaneous speed of a particle is defined as the magnitude of its instantaneous velocity 6

7. www.soran.edu.iq One-Dimensional motion with constant acceleration week3 7  A simple type of one-dimensional motion is that in which the acceleration is constant.  In this case the average acceleration ā x over any time interval is numerically equal to the instantaneous acceleration a x at any instant within the interval, and the velocity changes at the same rate through the motion (ā x = a x ).  If t i = 0 and t f any later time t, we find that a x = (v xf – v xi ) / (t – 0)  or v xf = v xi + a x t (for constant a x ) ……… (2.7)

8. www.soran.edu.iq 3. Vectors Week4 3.1 Coordinate systems 3.2 Vector and scalar quantities 3.3 Some properties of vectors 3.4 Components of a vector and unit vectors 3.5 Vector product (multiplication) 8

9. www.soran.edu.iq Coordinate systems (a) Cartesian coordinate  This system of coordinate is represented by two or three dimensions, i.e., plane or space.  In two dimensions (see the figure), the vector from the origin O = (0,0) to the point A = (2,3) is simply written as a = (2,3) 9

10. www.soran.edu.iq 3.2 Vector and scalar quantities 1. The scalar and vector quantities  The scalar quantity is that quantity determines by magnitude only, such as, temperature T and energy E.  The vector quantity is that quantity determines by magnitude and direction, such as, displacement x, velocity v, and force F.  A vector is a geometric entity characterized by a magnitude (in mathematics a number, in physics a number times a unit) and a direction.magnitude  In rigorous mathematical treatments, a vector is defined as a directed line segment, or arrow, in a Euclidean space. Week5 10 The Addition and subtraction of vectors A and B are two vectors, their sum is R, i.e., R = A + B Vectors can be subtracted, i.e., if A and B are two vectors then their subtraction is C = A – B = A + (-B)

11. www.soran.edu.iq 3.4 Components of a vector and unit vectors Components of a vector The components of the vector A in two dimensions are the vectors A x and A y, in such a way that: A = A x + A y A x = A cos θ A y = A sin θ A = [(A x ) 2 + (A y ) 2 ] ½ tan θ = A y / A x θ = tan -1 (A y / A x ) Week6 11

12. www.soran.edu.iq Unit vectors Another way to express a vector in three dimensions is to introduce the three standard basis vectors: standard basis e 1 = (1,0,0), e 2 = (0,1,0), e 3 = (0,1,0) These have the intuitive interpretation as vectors of unit length pointing up the x, y, and z axis of a Cartesian coordinate system, respectively, and they are sometimes referred to as versors of those axes.Cartesian coordinate system versors In terms of these, any vector in three dimensions space can be expressed in the form: (a,b,c) = a(1,0,0) + b(0,1,0) + c(0,0,1) = ae 1 + be 2 + ce 3 These three special vectors are often instead denoted i, j, k, the versors of the three dimensional space (or ), in which the hat symbol (^) typically denotes unit vectors (vectors with unit length).versorsunit vectors The notation e i is compatible with the index notation and the summation convention commonly used in higher level mathematics, physics, and engineering. index notationsummation convention 12

13. www.soran.edu.iq Vectors product (multiplication) 13

14. www.soran.edu.iq 4. Motion in two dimensions Week7 4.1 The position, Velocity, and Acceleration Vectors 4.2 Two-dimensional motion with constant acceleration 4.3 Projectile motion 4.4 Uniform circular motion 4.5 Tangential and radial acceleration 14

15. www.soran.edu.iq 4.1 The position, velocity, and acceleration vectors We describe here the motion of a particle in two dimensions, i.e., motion in xy-plane. The description of the position of a particle is by position vector r. The displacement vector ∆r is defined as the difference between its final position vector and its initial position vector: Displacement vector ∆r ≡ r f – r i ………………….. (4.1) The direction of ∆r is shown in the Figure below. 15

16. www.soran.edu.iq Two-dimensional motion with constant acceleration Week8 4.2 Two-dimensional motion with constant acceleration The position vector for a particle moving in the xy-plane can be written as r = xi + yj ………………. (4.6) where x, y and r change with time as the particle moves. From the Equations 4.3 and 4.6 the velocity of the particle can be obtained as v =dr/dt =dx/dt i +dy/dt j = v x i + v y j ………….. (4.7) Because the acceleration is constant, its components a x and a y are also constants. Therefore, the equations of kinematics to the x and y components of the velocity vector can be applied. 16

17. www.soran.edu.iq 4.4 Uniform circular motion Week9 17 4.4 Uniform circular motion The movement of an object in a circular path with constant speed v is called uniform circular motion. Even though an objects move at constant speed in circular path, it still has acceleration. The acceleration depends on the change in the velocity vector. The acceleration depends on the change in the magnitude of the velocity and / or by a change in the direction of the velocity. The change in the direction of the velocity occurs for an object moving with constant speed in a circular path. The velocity vector is always tangent to the path of the object and perpendicular to the radius of the circular path.

18. www.soran.edu.iq Laws of motion (Particle’s dynamics) ] Week10 18 5.1 The concept of the Force  An object accelerates due to an external force.  The object accelerates only if the net force acting on it is not equal zero.  The net force acting on an object is defined the vector sum of all forces acting on the object.  The net force is the total force, the resultant force, or the unbalanced force.  If the net force exerted on an object is zero, the acceleration is zero and its velocity remains constant. Definition of equilibrium  When the velocity of an object is constant (including when the object is at rest), the object is said to be in equilibrium.

19. www.soran.edu.iq 5.2 Newton’s first law “In the absence of external force, when viewed from an inertial reference frame, an object at rest remains at rest and an object in motion continues in motion with constant velocity”. That is to say, when no force acts on an object, the acceleration of the object is zero. From the first law, we conclude that any isolated object (one that does not interact with its environment) is either at rest or moving with constant velocity. Definition of inertia The tendency of an object to resist any attempt to change its velocity is called inertia 19

20. www.soran.edu.iq 5.3 Mass Definition of mass “Mass is an inherent property of an object and is independent of the object’s surrounding and of the method used to measure it”. Mass is a scalar quantity Mass and weight are two different quantities The weight of an object is equal to the magnitude of the gravitational force exerted on the object and varies with location. For example, a person who weight 900 N on the Earth weights only 150 N on the Moon. The mass of an object is the same everywhere: an object having a mass of 2 kg on the Earth also has a mass of 2 kg on the Moon. 20

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22. www.soran.edu.iq 5.5 The Gravitational force and weight Week11 22  The attraction force exerted by the Earth on an object is called the gravitational force F g.  This force is directed toward the center of the Earth, and its magnitude is called the weight of the object.  Freely falling object experience an acceleration g acting toward the center of the Earth.  Applying Newton’s second ΣF = ma to the freely falling object of mass m, with a = g and ΣF = F g, we obtain F g = mg …………………… (5.4)  Thus, the weight of an object, being defined as the magnitude of F g, is equal to mg, and g = 9.8 m/s 2.

23. www.soran.edu.iq 5.6 Newton’s third law Newton’s third law states that: If two objects interact, the force F 12 exerted by object 1 on object 2 is equal in magnitude and opposite in direction to the force F 21 exerted by object 2 on object 1: F 12 = - F 21 …………… (5.5) The force that object 1 exerts on object 2 is called the action force and the force of object 2 on object 1 the reaction force. Either force can be labeled the action or reaction force. In general, “The action force is equal in magnitude to the reaction force and opposite in direction”. The action and reaction forces act on different objects 23

24. www.soran.edu.iq 5.7 Some applications of Newton’s laws Week12 24 Objects in Equilibrium  If the acceleration of an object is zero; the particle is in equilibrium. If apply the second law to the object, noting that a = 0, we see that because there are no forces in the x direction, ΣF x = 0  The condition ΣF y = ma y = 0 gives ΣF y = T – F g = 0 or T = F g  The forces T and F g are not an action-reaction pair because they act on the same object.  The reaction force to T is T’, the downward force exerted by the object on the chain.  The ceiling exerts on the chain a force T” that is equal in magnitude to the magnitude of T’ and points in the opposite direction.

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26. www.soran.edu.iq Work and Energy Week13 6.1 Work done by a constant force If an object undergoes a displacement Δr under the action of a constant force F, the work done, W, by the force is, W = F Δr cos θ ………. (6.1) From Equation 6.1, the work done by a force on a moving object is zero when the force applied is perpendicular to the displacement of its point of application, i.e., θ = 90 o,then W = 0 because cos 90 o = 0. W = F Δr cos 90 o If the applied force F is in same direction as the displacement Δr, then θ = 0 and cos θ = 1. In this case, Equation 6.1 gives W = F Δr Work is scalar quantity, and its units are force multiplied by length. The SI unit of work is the newton. meter (N.m), this unit is called joule (J). 26

27. www.soran.edu.iq 6.2 Work done by a varying force Consider a particle being displaced along the x axis under the action of a force, F x, that varies with position, x. We can express the work done by F x as the particle moves from x i to x f as W = ∫ F x dx………. (6.2) This equation reduces to Equation 6.1 when the component F x = F cos θ is constant If more than one force acts on a particle, the total work done on the system is the work done by the net force. If the net force in the x direction is Σ F x then the total work, or net work, done as the particle moves from x i to x f is Σ W = W net = ∫ (∑ F x )dx ………….. (6.3) 27

28. www.soran.edu.iq 6.3 Kinetic energy and the Work–Kinetic energy Theorem Week14 28 6.3 Kinetic energy and the Work–Kinetic energy Theorem  Consider a system consisting of a single object.  The figure below shows a block of mass m moving through a displacement directed to the right under the action of a net force ΣF.  From Newton’s second law that the block moves with an acceleration a.  If the block moves through a displacement Δr = Δxi = (x f - x i )i the work done by the net force ΣF is

29. www.soran.edu.iq 6.5 Potential energy of a system Week15 We introduced the concept of kinetic energy associated with motion of objects. Now we introduce potential energy, the energy associated with the configuration of a system of objects that exert forces on each other. Potential energy Consider a system consists of an object and the Earth, interacting via the gravitational force. We do some work on the system by lifting the object slowly through a height Δy = y b – y a. While the object was at the highest point, the energy of the system had the potential to become kinetic energy, but did not do so until the book was allowed to fall. Thus, the energy storage mechanism before releasing the object is called potential energy. In this case, the energy is gravitational potential energy. 29

30. www.soran.edu.iq 7. Linear momentum and collision Week16 30 The momentum of an object is related to both its mass and its velocity. The concept of momentum leads us to second conservation law, that of conservation of momentum. We introduce a new quantity that describes motion, linear momentum. Consider two particles interact with each other. According to Newton’s third law, F 12 = – F 21 and then F 12 + F 21 = 0 m 1 a 1 + m 2 a 2 = 0 and

31. www.soran.edu.iq 7.2 Impulse and Momentum Week17 Assume that a single force F acts on a particle and that this force may vary with time. According to Newton’s second law, F = dp/dt, or dp = Fdt …………………… (7.7) If the momentum of the particle changes from p i at time t i to p f at time t f, then The quantity is called the Impulse of the force F acting on a particle over the time interval Δt = t f –t i Impulse is a vector defined by 31

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33. www.soran.edu.iq 7.3 Collisions in One Dimension  Week18 We use the law of conservation of linear momentum to describe what happens when two particles collide. There are two types of collision, elastic and inelastic. An elastic collision between two objects is one in which the total kinetic energy (as well as total momentum) of the system is the same before and after the collision. 33

34. www.soran.edu.iq Week19 Fluid statics: study of fluids at rest Different from fluid dynamics in that it concerns pressure forces perpendicular to a plane (referred to as hydrostatic pressure) If you pick any one point in a static fluid, that point is going to have a specific pressure intensity associated with it: P = F/A where P = pressure in Pascals (Pa, lb/ft 3 ) or Newtons (N, kg/m 3 ) F = normal forces acting on an area (lbs or kgs) A = area over which the force is acting (ft 2 or m 2 ) 34 Fluid Statics

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36. www.soran.edu.iq Bernoulli’s Equation Week20 Z 1 + ( P 1 /  ) + (V 1 2 /2g) = Z 2 + ( P 2 /  ) + (V 2 2 /2g) Wow! Z = pressure head, V 2 /2g = velocity head (heard of these?), 2g = (2)(32.2) for Eng. System If we’re trying to figure out how quickly a tank will drain, we use this equation in a simplified form: Z = V 2 /2g Example: If the vertical distance between the top of the water in a tank and the centerline of it’s discharge pipe is 14 ft, what is the initial discharge velocity of the water leaving the tank? Ans. = 30 ft/s Can you think of any applications for this? 36

37. www.soran.edu.iq Stagnation Point: Bernoulli Equation Stagnation point: the point on a stationary body in every flow where V= 0 Stagnation Streamline: The streamline that terminates at the stagnation point. Symmetric: Axisymmetric: If there are no elevation effects, the stagnation pressure is largest pressure obtainable along a streamline : all kinetic energy goes into a pressure rise: Total Pressure with Elevation: Stagnation Flow I: Stagnation Flow II: