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Lecture 3: Kinematics in One Dimension & Forces and Newton’s Laws of Motion Displacement, Velocity and Acceleration Displacement: X = X – X0 Average Velocity: X X 0 X (m/s) t t0 t X Instantaneous Velocity: V lim (m/s) t 0 t v v0 v Average Acceleration: a (m/s2) t t0 t v Instantaneous Acceleration: a lim (m/s2) t 0 t Equations of Kinematics in Two Dimensions X direction Y direction x x x y y y x Y y x y Y x x y y Y x x x y y y Applying the Equations of Kinematics in Two Dimensions 1 Make a drawing to represent the situation being studied. . 2 Decide which directions are to be called positive (+) and negative (–) relative to a . conveniently chosen coordinate origin. Do not change your decision during the course of a calculation. 3 Remember that the time variable t has the same value for the part of the motion along . the x axis and the part along the y axis. 4 In an organized way, write down the values (with appropriate + and – signs) that are . given for any of the five kinematic variables associated with the x direction and the y direction. Be on the alert for “implied data,” such as the phrase “starts from rest,” which means that the values of the initial velocity components are zero: v0x = 0 m/s and v0y = 0 m/s. The data summary boxes used in the examples are a good way of keeping track of this information. In addition, identify the variables that you are being asked to determine. 5 Before attempting to solve a problem, verify that the given information contains values . for at least three of the kinematic variables. Do this for the x and the y direction of the motion. Once the three known variables are identified along with the desired unknown variable, the appropriate relations from Table 3.1 can be selected. 6 When the motion is divided into “segments,” remember that the final velocity for one . segment is the initial velocity for the next segment. 7 Keep in mind that a kinematics problem may have two possible answers. Try to . visualize the different physical situations to which the answers correspond. Projectile Motion Projectile motion: two separate one dimensional motion X direction: X, ax, Vx, t where ax=0, Vx = constant Y direction: Y, ay, Vy, t where ay = 9.8 m/s2 and Vy is not a constant http://galileo.phys.virginia.edu/classes/109N/more _stuff/Applets/ProjectileMotion/enapplet.html Projectile Motion Break up the motion into X and Y direction Horizontal Direction: V final = V initial, acceleration in x direction = zero. Vertical direction: Feels the effect of gravity, Y component of velocity is not a constant Forces and Newton’s Laws of motion • Force: Push or pull • Contact force versus non-contact force (effect of gravity on sky diver) • Mass – scalar quantity • 17th century – Sir Isaac Newton – developed on the theories of Galileo • Came up with three important laws that deals with forces and masses • Newton’s laws of motion: Provides the basis for understanding the effect that forces have on an object Sir Isaac Newton Born: 4 Jan 1643 in Woolsthorpe, Lincolnshire, England Died: 31 March 1727 in London, England Newton’s First Law • An object continues in a state of rest or in a state of motion at a constant speed along a straight line, unless compelled to change that state by a net force. • Net Force = Vector Sum of all forces • State of rest and a state of constant velocity are equivalent. • Purpose of Net Force – to change velocity Newton’s First Law • Inertia: Natural tendency of an object to remain at rest or in motion at a constant speed along a straight line. • Newton’s 1st law is also called the law of inertia. • Mass of an object is a quantitative measure of the inertia (UNITS: Kg) • Mass and Weight are not interchangeable • Inertial frame of reference? Newton’s Second Law • 2nd law deals with what happens when a net force acts on the object • Greater force produces greater acceleration • Same net force will exert lesser acceleration on a massive object. • Net Force = F • Mass is another component that determines the acceleration. • F UNIT: Kg m/s2 = Newton a or F ma m Vector Nature of Newton’s Laws F ma Fx ma x F y ma y Newton’s Third Law • Whenever one body exerts a force on a second body, the second body exerts an oppositely directed force of equal magnitude on the first body. • Also called “Action- Reaction” law. • Every action has an equal and opposite reaction.