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Chapter 2 – Describing Motion.docx

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PHYS 101
Kenneth Ragan

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Chapter 2 – Describing Motion: Kinematics in One Dimension September 1, 2011 Mechanics: study of the motion of objects, and the related concepts of force and energy, can be divided into two parts  Kinematics: description of how objects move  Dynamics: deals with force and why objects move as they do Translation motion: objects that move without rotating Point particle: mathematical point and to have no spatial extent (no size) can only undergo translational motion  Particle model is useful when the object’s size is not so significant Basic Concepts in Kinematics: Distance [m] : SCALAR Displacement [m] : VECTORS Speed [m/s] : SCALAR Velocity [m/s] : VECTORS Reference Frame and Displacement: Any measurement of position, distance or speed must be made with respect to a reference frame or frame of reference. Example: A person walks toward the front of a train at 5 km/h. The train is moving 80 km/h with respect to the ground, so the walking person’s speed relative to the ground is 85km/h. In physics, we often draw a set of coordinate axes to specify the direction of the motion and to represent a frame of reference. In three dimensions a z-axis perpendicular to the x and y axes is added. For one-dimensional motion, we often use the x axis as the line along which the motion takes place. Then the position of an object at any moment is given by its x coordinate. If the motion is vertical, as for a dropped object, we usually use the y-axis. Distance: total length of the trajectory Displacement: the net change in position of the object, how far the object is from its starting point Example: A person walks 70m east, the 30m west. The total distance traveled is 100m but the displacement, shown as a blue arrow, is 40m to the east. Displacement is a quantity that has both magnitude and direction, such quantities are called vectors. x1 x2 Δx = x2– x1 10 m 30 m Δ means final value minus initial value (change in) Average Velocity: The term speed refers to how far an object travels in a given time interval, regardless of direction. Average speed is defined by the total distance traveled along its path by the time it takes to travel this distance.  Average Speed = Distance Traveled/Time Elapsed Speed is a positive number, with units. Velocity is used to signify both the magnitude of how fast an object is moving and also the direction in which it is moving (therefore a vector). Average velocity is defined in terms of displacement, rather than total distance traveled. Average Velocity = Displacement/Time Elapsed = Final Position – Initial Position/Time Elapsed The elapsed time, or time interval, t2– t1is the time that has passed during our chosen period of observation 2.3 - Instantaneous Velocity: The velocity at any given time, the average velocity during an infinitesimally short time interval. v = lim Δx Δt  0 Δt Can displacement and velocity have different signs (ie, be in different directions)?  Yes 2.4 – Acceleration Acceleration specifies how rapidly the velocity of an object is changing. Average Acceleration is defined as the change in velocity divided by the time taken to make this change:  Average Acceleration = Change of velocity/Time Elapsed Acceleration is also a vector, but for one-dimensional motion, we need only use a plus or minus sign to indicate direction relation to a chosen coordinate system. Instantaneous Acceleration can be defined in analogy to instantaneous velocity: a = lim Δv Δt 0 Δt Normal units of acceleration in MKS:  m/s 2  acceleration due to gravity 9.8 m/s Decleration is often used when an object is slowing down, means that the magnitude of the velocity is decreasing; it does not necessarily mean it is negative 2.7 – Falling Objects Galileo Galilei (father of modern science) discovered: o The speed of a falling object is NOT proportional to its mass or weight o All objects, light or heavy, fall with the same acceleration, in the absence of air Example: A ball and a light piece of paper are dropped at the same time – The baseball hits the ground first. Repeated, with the paper wadded up – They both reach the ground at the same time. Galileo’s hypothesis: free fall is at constant acceleration – at a given location on the Earth and in the absence of air resistance, all objects fall with the same constant acceleration. We call this acceleration due to gravity on the Earth (represented by the symbol g) with an approx. magnitude of 9.80 m/s 2 2.8 – Graphical Analysis of Linear Motion Example: Graph the displacement: time is independent variable (x-axis) and displacement is on the y-axis Slope = (change in displacement)/(change in time) = velocity! Displacement-vs-time graphs can be used to calculate the velocity-vs-time graphs Quiz Results Reshmi & Sarah on their bikes:  Velocity vs. Time graph  If displacement’s are the same, R is moving faster  Sarah will always win short distance races  Reshmi will always win long distance races  Therefore you cannot tell who will win Velocity Time 34, 501, 798 / 80 seconds  Best answer: 34.5 Million people Quiz #2: Which of t
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