# DISPLACEMENT and DISTANCE

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DISPLACEMENT and DISTANCE

FISIKA 1 18 SEPTEMBER 2013 Fakultas Teknologi Pertanian UGM • • • • 20% : HOMEWORK / QUIZ 10% : CLASS ACTIVITY 35% : MIDTERM 35% : FINAL EXAM MOTION! Motion defined • Any change in position with respect to a frame of reference. • Frame of reference – any physical entity which could serve as basis in telling that an object is moving. Mechanics the branch of Physics that is concerned with the analysis of the action of forces on matter or material systems. • Dynamics is the branch of mechanics that is concerned with the effects of forces on the motion of a body or system of bodies, especially of forces that do not originate within the system itself. • Kinematics branch of mechanics that studies the motion of a body or a system of bodies without consideration given to its mass or the forces acting on it Unlocking of Difficulties • • • • • • • • Distance Displacement Speed Velocity Acceleration Deceleration Instantaneous Speed Instantaneous Velocity WHAT IS DIFFERENCE BETWEEN…. DISPLACEMENT and DISTANCE ???????? Displacement and distance To go to school from home... l2 your school your home l1 l3 Distance = length of path you travelled = l1 + l2 + l3 Displacement and distance To go to school from home... your home Size = length of this arrow your school displacement from home to school A displacement has size & direction. Displacement and distance Displacement requires : – Length of a straight line going from the old to the new positions i.e. size/magnitude – Direction of the movement Distance vs. Displacement Distance is the extent of space between two objects or places; an intervening space. It is also the total length traversed by a moving object. It is a scalar quantity. Displacement is the shortest length between two points. It is a vector quantity. Displacement along a straight line • Set an initial point, • Use positive (+) and negative (−) signs to represent the direction. * Remember assign a direction as positive! Displacement along a straight line Take the direction to the right as positive. Displacement along a straight line Displacement in a plane What is the total displacement of the car? Displacement in a plane Graphical method From O to A and then to B. 3 km 4 km 37 5 km N total displacement = 3 km to the east Algebraic method It is easy to add displacements if they are perpendicular to each other. e.g. N 3 km 5 2 = 42 + d 2 d = 3 km 4 km 37 5 km Speed vs. Velocity • Speed is the ratio of • Velocity is the ratio distance traveled to of change in time interval. It is a position to time scalar quantity. interval over which change takes place. It is a vector quantity. the two terms can just be interchanged in an ordinary conversation, but they should have a distinction in Physics. WHAT IS DIFFERENCE BETWEEN…. VECTOR and SCALAR ???????? Vectors • A scalar quantity is one that is represented by a single number – mass; length; time; temperature; volume; energy; charge; etc. • A vector is a quantity which has both magnitude and direction. – Velocity, Displacement, Momentum, Force, … • In physics we need vectors because the real world is (at least) 3 dimensional. Location in Space • To locate an object in space we need to establish a coordinate system with an origin and axes. • Points are located by giving their x and y (and z) coordinates. A vector describes a displacement or from one point to another y The components of the vector describe the displacement in the x and y direction. 7 A (1,5) 6 5 4 3 2 1 C VAB=(4,-2) B Two vectors are parallel if they describe (5,3) the same displacement even if that displacement begins at different points. (3,2) x origin 1 2 3 4 5 6 7 Vector Addition A+B=C Geometrically: Parallel transport the tail of B to the head of A. The sum goes from the tail of A to the head of B. Note: This construction only works if head of A is at the tail of B. Otherwise you need to move B to make that true Algebraically: Add the components C(3,5) B(-2,4) A (5,1) A 5 B -2 C 3 1 4 5 Vector addition is commutative and associative Problem Given that q = +12 mC and d = 16 cm, (a) find the direction and magnitude of the net electrostatic force exerted on the point charge q2 in Figure below. (b) (b) How would your answers to part (a) change if the distance d were tripled? Solution Draw free body for JUST q2 F21 k (12mC ) 24mC (0.16m) 2 in direction from 1 to 2 101N xˆ F23 k (24mC ) 36mC (0.16m) 2 in direction from 3 to 2 303N xˆ Solution, cont’d F2 (101N 303N ) xˆ 202N in x - direction B) Tripling the separations decreases all forces by a factor of 32=9 F2 = 22.4 N, +x direction Distance and Displacement • A physics teacher walks 4 meters East, 2 meters South, 4 meters West, and finally 2 meters North. • 1. What is the distance? • 2. What is the displacement? Distance and Displacement 1. What is the distance? 2. What is the displacement? Speed and Velocity • The skier has an average speed of • (420 m) / (3 min) = 140 m/min and an average velocity of • (140 m, right) / (3 min) = 46.7 m/min, right Velocity along a straight line Take direction towards right as positive