Phy 101 - General Physics I PDF

PHY 101-GENERAL PHYSICS I LECTURE – PART A  OUTLINE SPACE AND TIME: UNITS AND DIMENSION VECTOR AND SCALAR: DIFFERENTIATION OF VECTORS: DISPLACEMENT, VELOCITY AND ACCELERATION KINEMATICS: NEWTON’S LAW OF MOTION RELATIVE MOTION APPLICATIONS OF NEWT...

PHY 101-GENERAL PHYSICS I LECTURE – PART A  OUTLINE SPACE AND TIME: UNITS AND DIMENSION VECTOR AND SCALAR: DIFFERENTIATION OF VECTORS: DISPLACEMENT, VELOCITY AND ACCELERATION KINEMATICS: NEWTON’S LAW OF MOTION RELATIVE MOTION APPLICATIONS OF NEWTONIAN MECHANICS EQUATION OF MOTION CONSERVATION PRINCIPLES IN PHYSICS: CONSERVATIVE FORCES, CONSERVATION OF LINEAR MOMENTUM, KINETIC ENERGY AND WORK, POTENTIAL ENERGY  SPACE AND TIME- UNITS AND DIMENSION In Physics any quantity that has a measurable property is known as a physical quantity. Physical quantity can be classified into two: fundamental and derived quantity.  FUNDAMENTAL QUANTITIES AND UNITS Fundamental quantities are independent quantities or that do not depend on any other quantities for their derivations and their units are called fundamental units. Examples are Quantity Unit Symbol Time seconds S Mass kilogram Kg Length metre M Temperature kelvin K Electric current Ampere A Amount of substance Mole Mol Luminous Intensity Candela Cd  DERIVED QUANTITIES AND UNITS Derived quantities are those quantities that derived from the fundamental quantities. Their units are known as derived units. Examples are: Quantity Formula Unit Symbol Area Length x length Metre squared m2 Volume Length x length x length Metre cubed m3 Speed Distance/Time Metre per second m/s or ms-1 Velocity Displacement/Time Metre per second m/s or ms-1 Acceleration Velocity/Time Metre per second squared m/s2 or ms-2 Force Mass x acceleration Newton N Work Force x Distance Newton-metre or Joule Nm or J Density Mass/Volume Kilogram per metre cubed Kgm-3 Pressure Force/Area Newton per metre squared Nm-2 Momentum Mass x velocity Kilogram-metre per second Kgms-1  DIMENSIONS Dimensions are the powers to which fundamental quantities are raised to represent a particular quantity. Physical Quantity Dimensional Formula Area [L2] Volume [L3] Velocity [LT-1] Acceleration [LT-2] Force [MLT-2] Work [ML2T-2] Momentum [MLT-1]  USES OF DIMENSIONS TO DETERMINE THE TRUE RELATIONSHIP BETWEEN PHYSICAL QUANTITIES HELPS TO DETERMINE THE APPROPRIATE UNIT OF A PHYSICAL QUANTITY TO CHECK THE ACCURACY OF PHYSICAL QUANTITIES.  EXAMPLES 1. WHAT IS THE DIMENSION OF PRESSURE PRESSURE = FORCE/AREA, P = F/A BUT F = [MLT-2], A = [L2] P = 2 = 𝑀𝐿−1𝑇−2 𝑀𝐿𝑇 −2 𝐿   VECTORS AND SCALAR Scalar is a quantity with magnitude but no direction. E.g. distance, time, temperature, area, volume, electric current, energy, speed e.t.c. Vector is a quantity with both magnitude and direction. E.g displacement, force, velocity, acceleration, momentum etc.  VECTOR REPRESENTATION Vectors can be represented in the following ways. A A  VECTOR RESOLUTION VECTORS CAN BE RESOLVED INTO: VERTICAL AND HORIZONTAL COMPONENTS  HORIZONTAL COMPONENT WHERE A IS THE MAGNITUDE OF THE VECTOR HORIZONTAL COMPONENT VERTICAL COMPONENT  THE RESULTANT VECTOR FOR 2-D The magnitude of vector A is given as: We can write for 2-D FOR 3-D Magnitude of A A can be resolved as  VECTOR DIRECTION In 2-D, the angle that vector A makes with the positive x- axis is given as:  UNIT VECTOR A unit vector is a vector having a unit magnitude. It is used to describe the direction of the vector. It is given as: = but Therefore Where are called direction cosines of vector A  LET’S TAKE A LOOK AT THE PROBLEM BELOW  VECTOR ADDITION The process in which to or more vectors are added to get a single vector is called vector addition. This single vector is known as resultant vector. It has the same effect as the other vectors combined together. Vectors can be added graphically by head to tail rule. According this rule, addition of vector A and B can be done by 1. Placing the tail of B on the head of A 2. Drawing a line from the tail of A to the head of B. is line is the sum of vectors A and B called the resultant vector.  N.B: A + B and B + A have the same resultant. We can write A + B = B + A Therefore vector addition is cummutative  VECTORS CAN ALSO BE ADDED COMPONENT-WISELY Two vectors A and B are give as A = 2i + 3j + 2k and B = i + 2j + 4k. Find the value of A +B SOLUTION GIVEN: A = 2i + 3j + 2k , B = i + 2j + 4k. A +B = (2i + 3j + 2k )+ (i + 2j + 4k) Adding i to i, j to j and k to k = 2i +i + 3j + 2j +2k + 4k = 3i + 5j + 6k N.B: Addition of vector gives a vector  VECTOR DIFFERENTIATION  EXAMPLE  KINEMATICS Kinematics: is the study of motion of a body without the consideration of its cause. Motion is the change of a body position with time. Motion can be: translational, oscillatory, random or rotational.  NEWTON’S LAWS OF MOTION FIRST LAW: A body continues to be in its state of rest or in uniform motion along a straight line unless an external force is applied to it. This law is know as the law of inertia. INERTIA: this is the tendency of a body at rest to remain at rest and a body motion to continue moving with unchanged velocity. Inertia is a measure of mass of a body. EXAMPLE : if a moving vehicle suddenly stops then the passengers inside the vehicle bend outward.     THIRD LAW: For every action there is an equal and opposite reaction. Example: recoil of gun, jet propulsion.  RELATIVE MOTION Relative motion is the motion of a body with respect to another. The velocities of the bodies are relative to each other. The relative velocity of object A with respect to object B is VAB = VA – VB When two objects are moving in the same direction VAB = VA – VB When two objects are moving in different direction VAB = VA + VB When the two objects are moving at an angle to each other  APPLICATION OF NEWTONIAN MECHANICS EQUATIONS OF MOTION     VELOCITY TIME GRAPH This is the graph of velocity against time. The slope of this graph gives the acceleration of the motion. DIFFERENCE VELOCITY – TIME GRAPH 1. Object moving with constant velocity 2. Object accelerating uniformly from rest 3. Object moving with uniform retardation Object moving with increasing Object moving with decreasing acceleration acceleration  A car starts from rest at point A at Godfrey Okoye University main gate and comes to rest at point B at Godfrey Okoye University campus II gate 2km away in 3 minutes. It has first a uniform acceleration for 40s, then a uniform speed and is brought to rest with constant deceleration after 20s. (i) Represent the motion in a velocity time graph. (ii) determine the maximum speed (iii) find the deceleration. Solution (i)     MOTION IN TWO OR THREE DIMENSION  PROJECTILE MOTION  TIME OF FLIGHT  HORIZONTAL RANGE  MAXIMUM HEIGHT  EXAMPLES    PROJECTILE PROJECTED FROM SOME HEIGHT   CONSERVATION PRINCIPLE IN PHYSICS CONSERVATIVE FORCE: This is such force for which the work done by this force on a particle moving between any two points is independent of the path taken by the particle. The work done by a conservative force on a particle moving through any closed path is zero. Examples of conservative force are: Gravity Spring force  NON CONSERVATIVE FORCE: A non conservative force does not satisfy the condition of conservative force. This force acting in a system causes changes in the mechanical energy of a system. Examples of non conservative forces are Friction Tension  CONSERVATION OF LINEAR MOMENTUM Momentum is the product of mass and velocity. Its unit is kgm/s.