Lecture 2 Representing Motion PDF

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10/5/20

Lecture 2: Representing Motion Sections 1.1-1.6

What general ways can we think to describe any type of motion?

•Motion: A First Look •Position and Time: Putting Numbers on Nature •Velocity •A Sense of Scale: Significant Figures, Scientific Notation, and Units

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Learning objectives §Represent and analyze a motion of an object using the particle model and motion diagrams. §Describe motion in terms of position, displacement, and velocity in a defined coordinate system. §Distinguish between distance and displacement, and between speed and velocity. §Express quantities using scientific notation and correct units.

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Types of Motion Motion is the change of an object’s position or orientation with time. The path along which an object moves is called the object’s trajectory.

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Discussion 1: Motion Diagrams Snapshots of the object are taken at equal time motion based on such composite diagrams? For skater? Runner? Car?

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Motion Diagrams and The Particle Model The particle model of motion is a simplification in which we treat a moving object as if all of its mass were concentrated at a single point. In such diagrams, the time interval ∆𝑡 = 𝑡! − 𝑡" is always positive, and the time between snapshots is the same.

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Two runners jog along a track. The positions are shown at 1 s intervals. Which runner is moving faster?

a.

Runner A

b. Runner B

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Position and Coordinate Systems To specify position we need a reference point (the origin), a distance from the origin, and a direction from the origin. The combination of an origin and an axis marked in both the positive and negative directions makes a coordinate system.

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Displacement: Change in Position A change of position is called a displacement. Displacement is the difference between a final position and an initial position:

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𝑥1 = 5

𝑥2 = 7 𝑥 [cm]

2 Consider the positions shown. 1.

What’s the displacement we make in going from 𝑥# to 𝑥$ ?

2. What about going from 𝑥$ to 𝑥# ? 3.

What’s the distance between 𝑥# and 𝑥$ ?

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Does the displacement of an object depend on the specific location of the origin of the coordinate system?

a.

Yes

b. No c.

It depends on the coordinate system.

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An ant crawling along the floor follows a semi-circular path, going half way around the circumference of a circle of radius 𝑅. The distance traveled, and the displacement of the ant, are respectively:

a.

𝜋𝑅 and 𝜋𝑅

b.

2𝑅 and 𝜋𝑅

c.

𝜋𝑅 and 2𝑅

d.

𝜋𝑅 and zero

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Speed vs. Velocity Motion at a constant speed in a straight line is called uniform motion.

Speed measures only how fast an object moves, but velocity tells us both an object’s speed and its direction. The velocity defined by Equation 1.2 is called the average velocity.

speed =

distance traveled in a given time interval time interval

velocity =

Speed of an object in uniform motion

Speed is a scalar quantity.

displacement ∆𝑥 = ∆𝑡 time interval

Velocity of a moving object Velocity is a vector quantity; one that depends on both magnitude AND direction. A speedometer in the car measures speed not velocity

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Speed of blood in circulatory system §Speed of blood in circulatory system changes. §The blood flow is slowest at capillaries which is good for exchange of materials between tissues and blood.

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A car travels from 𝑥# = 2 km to 𝑥$ = 5 km in 3 minutes, then to 𝑥' = −4 km in 12 minutes. What’s car’s the displacement in kilometers? What is the car’s velocity in km/min?

a.

∆𝑥 = 6 km, 𝑣 = 0.4 km/min

b.

∆𝑥 = −6 km, 𝑣 = −0.4 km/min

c.

∆𝑥 = 12 km, 𝑣 = 0.8 km/min

d.

∆𝑥 = −12 km, 𝑣 = −0.8 km/min

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Units, using prefixes, and unit conversion The SI units is a set of standards established by international committee. ◦ Length in meters (m) ◦ Mass in kilograms (kg) ◦ Time in seconds (s)

US is of of 3 countries world-wide that don’t use SI units! Importance of having units: https://en.wikipedia.org/wiki/Mars_Climate_Orbiter https://www.youtube.com/watch?v=zN9LZ3ojnxY

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