Kinematics - Lecture Note

KINEMATICS Kinematics is a branch of mechanics. It is the science of describing the motion of objects using words, diagrams, numbers, graphs, and equations. Its goal is to describe and ultimately explain the motion of real-world objects. The mathematical quantities that are used to described the motion of objects can be divided into two categories; scalar and vector. Note: Motion is the action of changing position or location. An object is in motion if its position changes in relation to some fixed object during a given time Scalar and Vector Quantities SCALAR: It has magnitude, a numerical value and unit of quantity. It has a value but no direction. • Distance, Speed, Mass, Energy, Density, Power, Length, Area, Volume, Time, Temperature, Work Symbol d v t E Names of Scalars Distance Speed Time Energy Example 30 m 50 m/s 15 s 2000 cal VECTOR: It has both magnitude and direction. • Displacement, Velocity, Weight, Acceleration, Force, Impulse, Pressure, Momentum, Gravity, Drag Symbol d v F a Names of Vectors Displacement Velocity Force Acceleration Example 30 m North 50 m/s West 100 lb up 12 m/s2 down Distance vs. Displacement: Distance and displacement are two quantities that may seem to mean the same thing yet have distinctly different definition and meanings. Distance (Scalar) • • Refers to “how much ground an object has covered” during its motion length of the actual paths traveled Displacement (Vector) • • Refers to “how far out of place an object is” objects change in position considering its staring and final position Speed vs. Velocity: Speed (Scalar): • • • • • Refers to “how fast an object is moving” Distance covered per unit of time A fast-moving object has a high speed and covers a relatively large distance in a short amount of time A slow-moving object that has a low speed; it covers a relatively small amount of distance in the same amount of time An object with no movement at all has a zero speed Velocity (Vector): • • • Refers to the “the rate at which object changes its position” Speed + Direction Even if the object is slowing down and the magnitude of velocity is decreasing, its direction would still be the same as the direction in the object is moving Acceleration: • • • • • • The rate at which an object changes its velocity An object is accelerating if it is changing its velocity A change in direction (from East to North-East) A change in both speed and direction (from 34 km/h East to 12 km/h West) A change in speed, the magnitude of the velocity (from 34 km/h to 67 km/h) If an object is not changing its velocity, then the object is not accelerating REPRESENTING VECTORS: Vector quantity is represented by an arrow. The point where the arrows start is called the initial point and the point where the arrow ends is called the terminal point. The magnitude of a vector in a scaled vector diagram is depicted by the length of the arrow. The arrow is drawn a precise length in accordance with a chosen scale. In vector diagrams, the arrow direction represents the direction of motion (here, East), and the arrow length represents the magnitude (here, 15 km). The chosen scale is: 1 cm on the diagram = 3 km in reality. Vector Addition: Two results can be added together to determine the result (or resultant). Conditions to be followed while adding actors are: • • can be added only if they are of the same nature cannot add vectors and scalars together 1. TAIL-HEAD METHOD • When adding vectors, place the tail of the second vector at the head of the first vector. • The resultant is the results of adding two or more vectors. It is the sum of the vectors. • The image illustrates a vector with a given scale of 1 cm = 10 m representing 50m with an angle of 30 degree towards West. 2. PARALLELOGRAM METHOD • It is used to add two vectors when the vectors that are to be added form the two adjacent sides of a parallelogram by joining the tails of the two vectors. Note: Calculate the displacement using the Pythagorean Theorem. c2 = a2 + b2 SAMPLE PROBLEMS I. Identify if the given is Scalar or Vector. __________1. 15 m/s North __________2. 37 degrees Celsius __________3. 100 Watts __________4. 50 km N of W __________5. 80 km / hr II. Illustrate the given. Also use the Pythagorean theorem for whichever question it applies to. (Use ruler and protractor) 1. Scale: 1 cm;10 km = 50 km Vector: 30o East 2. Scale: 1 cm:10 cm = 60 m Vector: 90o North ANSWER KEYS: I. 3. (Scale: 1cm;1N) Given: A=5N North B=10N West C=3N East D=7N South Find: a) A+D b) B+C c) A+B d) C+D 1. Vector II. 1. 2. 2. Scalar 3. Scalar 4. Vector 5. Scalar 3. a) b) c) C2 = a2 + b2 𝒄 = √𝟓𝟐 + 𝟏𝟎𝟐 𝒄 = √𝟐𝟓 + 𝟏𝟎𝟎 𝒄 = √𝟏𝟐𝟓 𝒄 = 𝟏𝟏. 𝟏𝟖 𝐍(𝐰𝐞𝐬𝐭) d) C2 = a2 + b2 𝒄 = √ 𝟑𝟐 + 𝟕𝟐 𝒄 = √𝟗 + 𝟒𝟗 𝒄 = √𝟓𝟖 𝒄 = 𝟕. 𝟔𝟐 𝐍(𝐬𝐨𝐮𝐭𝐡 𝐞𝐚𝐬𝐭)