Introduction to Mechanics Mechanics It has nothing to

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Introduction to Mechanics

Introduction to Mechanics

Mechanics • It has nothing to do with the people you call when your

Mechanics • It has nothing to do with the people you call when your car needs to be repaired. • It is the study of motion.

Historical Development of Mechanics Aristotle vs. Galileo

Historical Development of Mechanics Aristotle vs. Galileo

Aristotle He said that we must first understand why objects move.

Aristotle He said that we must first understand why objects move.

Aristotle • Things move because they “desire” to do so. • Light things “desire”

Aristotle • Things move because they “desire” to do so. • Light things “desire” to rise to the heavens. • Heavy things “desire” to sink to earth. • In short, objects have a natural tendency.

Aristotle Early scientists like Aristotle were called natural philosophers.

Aristotle Early scientists like Aristotle were called natural philosophers.

Galileo said that we should first study how things move, and then we should

Galileo said that we should first study how things move, and then we should describe why they move.

Mechanics the study of motion Dynamics Kinematics Why? cause How? Statics Stationary things react

Mechanics the study of motion Dynamics Kinematics Why? cause How? Statics Stationary things react to pushes and pulls.

Mechanics is the study of 1. 2. 3. 4. life. motion. work. systems. Question

Mechanics is the study of 1. 2. 3. 4. life. motion. work. systems. Question

T/F Aristotle believed that we should first determine why things move. T Question

T/F Aristotle believed that we should first determine why things move. T Question

System an artificial boundary used to isolate an object or objects

System an artificial boundary used to isolate an object or objects

Surroundings everything outside of the system

Surroundings everything outside of the system

Systems Scientists are free to select any system as they study the motion of

Systems Scientists are free to select any system as they study the motion of objects. Examples: you, your desk, the floor you and your desk

Frame of Reference • When a car zooms by you, it is moving.

Frame of Reference • When a car zooms by you, it is moving.

Frame of Reference • But if you are in the car, it seems that

Frame of Reference • But if you are in the car, it seems that the car is standing still and everything else is speeding past the windows.

Frame of Reference What’s the difference? your frame of reference

Frame of Reference What’s the difference? your frame of reference

Frame of Reference What is THE frame of reference? you (How self-centered!) the earth

Frame of Reference What is THE frame of reference? you (How self-centered!) the earth the sun the galaxy

Frame of Reference • There is no “THE frame of reference. ” • Choose

Frame of Reference • There is no “THE frame of reference. ” • Choose the best frame of reference for the problem being solved.

Frame of Reference The frame of reference you choose determines how the motion will

Frame of Reference The frame of reference you choose determines how the motion will be described. Sun North Pole Earth

Kinds of Reference Frames 1. Fixed—the reference frame is stationary, but the system moves.

Kinds of Reference Frames 1. Fixed—the reference frame is stationary, but the system moves. 2. Accelerated—the reference frame accelerates with the system. 3. Rotational—the reference frame accelerates, but the system is stationary.

Coordinate Axis Number Line • Zero is the origin. • Negative numbers are to

Coordinate Axis Number Line • Zero is the origin. • Negative numbers are to the left of the origin. • Positive numbers are to the right of the origin.

Time non-physical continuum that orders the sequence of events

Time non-physical continuum that orders the sequence of events

Time • sometimes called the spacetime continuum • created by God • Before time

Time • sometimes called the spacetime continuum • created by God • Before time was, God is. “I AM. ”

Time • Any event that happens must occur within a span of time. •

Time • Any event that happens must occur within a span of time. • The start of that time span is called the initial time (ti). • The end of that time span is called the final time (tf).

Time • The difference between the initial and final time is the time interval.

Time • The difference between the initial and final time is the time interval. • It is called Δt (“delta tee”) and is found by subtracting the initial time from the final time.

What is another name for a coordinate axis? 1. 2. 3. 4. fulcrum space-time

What is another name for a coordinate axis? 1. 2. 3. 4. fulcrum space-time continuum number line reference frame Question

Scalar measurement that has a magnitude (amount) with no direction indicated Examples: 13 m

Scalar measurement that has a magnitude (amount) with no direction indicated Examples: 13 m 47 km/h

Scalar Since the smallest measurement is zero, scalars never have a negative magnitude. This

Scalar Since the smallest measurement is zero, scalars never have a negative magnitude. This paper has a measurement of 215. 7 mm.

Vectors measurement that has both a magnitude and a direction Examples: 13 m forward

Vectors measurement that has both a magnitude and a direction Examples: 13 m forward 47 km/h ENE

Vectors The magnitude part of a vector is considered to be a scalar.

Vectors The magnitude part of a vector is considered to be a scalar.

Vectors • Vectors are shown force on the coordinate (F) axis by an arrow.

Vectors • Vectors are shown force on the coordinate (F) axis by an arrow. • The length indicates the magnitude. • The arrowhead indicates the weight direction. (w)

T/F Scalar measurements have magnitude and direction. F Question

T/F Scalar measurements have magnitude and direction. F Question

Kinematics: Describing Motion

Kinematics: Describing Motion

Motion • a change of position during a time interval • It can be

Motion • a change of position during a time interval • It can be in one, two, or three dimensions. X 1 = 0. 5 cm X 2 = 1. 5 cm X 3 = 2. 5 cm 0 cm 1 cm 2 cm 3 cm x v t 1 t 2 t 3

Distance a positive scalar quantity that indicates how far an object has traveled during

Distance a positive scalar quantity that indicates how far an object has traveled during a time interval

Displacement the overall change in position during a time interval (how much it moved)

Displacement the overall change in position during a time interval (how much it moved)

Displacement • Displacement is a vector quantity. • The distance is the magnitude of

Displacement • Displacement is a vector quantity. • The distance is the magnitude of the displacement vector.

X X

X X

Speed • the rate at which an object changes position • the distance traveled

Speed • the rate at which an object changes position • the distance traveled in a period of time • As an equation: distance d speed (v) = = time Δt

Speed d s t using the speed triangle: distance speed = time

Speed d s t using the speed triangle: distance speed = time

Speed d s t using the speed triangle: time = distance speed

Speed d s t using the speed triangle: time = distance speed

Speed d s t using the speed triangle: distance = speed × time

Speed d s t using the speed triangle: distance = speed × time

Sample Problem 1 If a motorcycle travels 540 km in 2 hours, what is

Sample Problem 1 If a motorcycle travels 540 km in 2 hours, what is its speed? distance 540 km speed = = time 2 h = 270 km/h

What does speed equal? 1. time / distance 2. the rate at which an

What does speed equal? 1. time / distance 2. the rate at which an object changes time 3. the amount of time traveled over a distance 4. distance / time Question

If a car travels 400 km and the trip takes 5 hours, how fast

If a car travels 400 km and the trip takes 5 hours, how fast is the car traveling? 1. 2. 3. 4. 405 km/h 395 km/h 2000 km/h 80 km/h Question

If an object is traveling at 100 km/h for 5 hours, how far does

If an object is traveling at 100 km/h for 5 hours, how far does it travel? 1. 500 km 2. 20 km d= s ×km t 3. 105 d = 100 km/h × 5 h 4. 95 km d = 500 km Question

Average Speed rate of motion over a time interval V= V 1 + V

Average Speed rate of motion over a time interval V= V 1 + V 2 2

Instantaneous Speed rate of motion at a specific time

Instantaneous Speed rate of motion at a specific time

Sample Problem 2 It takes a fast cyclist 0. 35 h (20. 85 min)

Sample Problem 2 It takes a fast cyclist 0. 35 h (20. 85 min) to cover the 19 km stage of a European biking race. What is his average speed in km/h? Known: time interval (Δt) = 0. 35 h distance (d) = 19 km Unknown: speed (v)

Sample Problem 2 Known: time interval (Δt) = 0. 35 h distance (d) =

Sample Problem 2 Known: time interval (Δt) = 0. 35 h distance (d) = 19 km Unknown: speed (v) d 19 km v= = = 54. 2 km/h Δt 0. 35 h = 54 km/h 2 Sig Digs allowed

Velocity • technically different than speed • involves both speed and direction • It

Velocity • technically different than speed • involves both speed and direction • It is the rate of displacement. • Example: The car is traveling east at 65 mph.

Velocity • Velocity is called a vector measurement because it includes how fast and

Velocity • Velocity is called a vector measurement because it includes how fast and which direction. • Speed is called a scalar measurement because it only involves how fast.

Scalars and Vectors Scalars Vectors distance (d) displacement (d) speed (v) velocity (v) Remember,

Scalars and Vectors Scalars Vectors distance (d) displacement (d) speed (v) velocity (v) Remember, vectors can be positive or negative, but scalars are only positive.

Scalars and Vectors Vfuel cell Vhybrid − 45 m/s +30 m/s West (−) East

Scalars and Vectors Vfuel cell Vhybrid − 45 m/s +30 m/s West (−) East (+)

Acceleration • Acceleration is an increase in velocity in a given space of time

Acceleration • Acceleration is an increase in velocity in a given space of time (speeding up). • Deceleration is a decrease in velocity in a period of time (slowing down).

Acceleration Formula Acceleration = change in velocity change in time The Greek letter delta

Acceleration Formula Acceleration = change in velocity change in time The Greek letter delta (Δ) stands for “change in. ” Δv Acceleration = Δt

Acceleration Units • The units for velocity are distance/time. • Since acceleration is velocity/time,

Acceleration Units • The units for velocity are distance/time. • Since acceleration is velocity/time, the units must be distance/time.

Acceleration Units • This is rewritten distance/time 2. • Actual units could be miles/sec

Acceleration Units • This is rewritten distance/time 2. • Actual units could be miles/sec 2. a v West (−) East (+)

Sample Problem 3 A car moving at +5. 0 m/s smoothly accelerates to +20.

Sample Problem 3 A car moving at +5. 0 m/s smoothly accelerates to +20. 0 m/s in 5. 0 s. Calculate the car’s acceleration. North is positive. Known: car’s vi = +5. 0 m/s car’s vf = +20. 0 m/s time interval (Δt) = 5. 0 s Unknown: acceleration (a)

Sample Problem 3 Known: car’s vi = +5. 0 m/s car’s vf = +20.

Sample Problem 3 Known: car’s vi = +5. 0 m/s car’s vf = +20. 0 m/s time interval (Δt) = 5. 0 s Unknown: acceleration (a) a= vf − v i Δt = (+20. 0 m/s) − (+5. 0 m/s) 5. 0 s

Sample Problem 3 a= a= vf − v i Δt = (+20. 0 m/s)

Sample Problem 3 a= a= vf − v i Δt = (+20. 0 m/s) − (+5. 0 m/s) +15. 0 m/s 5. 0 s = +3. 0 m/s/s = 3. 0 m/s 2 north

Sample Problem 4 A car moving at +20. 0 m/s smoothly slows to a

Sample Problem 4 A car moving at +20. 0 m/s smoothly slows to a stop (0 m/s) in 6. 0 s. Calculate the car’s acceleration. East is positive. Known: car’s vi = +20. 0 m/s car’s vf = 0. 0 m/s time interval (Δt) = 6. 0 s Unknown: acceleration (a)

Sample Problem 4 Known: car’s vi = +20. 0 m/s car’s vf = 0.

Sample Problem 4 Known: car’s vi = +20. 0 m/s car’s vf = 0. 0 m/s time interval (Δt) = 6. 0 s Unknown: acceleration (a) a= vf − v i Δt = (0. 0 m/s) − (+20. 0 m/s) 6. 0 s

Sample Problem 4 a= a= vf − v i Δt = (0. 0 m/s)

Sample Problem 4 a= a= vf − v i Δt = (0. 0 m/s) − (+20. 0 m/s) -20. 0 m/s 6. 0 s = -3. 3 m/s/s = -3. 3 m/s 2 west

What is acceleration? 1. 2. 3. 4. going a distance the direction you travel

What is acceleration? 1. 2. 3. 4. going a distance the direction you travel how fast you move a change in how fast you move Question

If a car takes 5 seconds to change speed by 40 m/s, what is

If a car takes 5 seconds to change speed by 40 m/s, what is its acceleration? 1. 2. 3. 4. 8 m/s 2 45 m/s 2 35 m/s 2 200 m/s 2 Question

A car going 40 m/s takes 10 s to speed up to 140 m/s.

A car going 40 m/s takes 10 s to speed up to 140 m/s. What is its acceleration? 1. 2. 3. 4. 400 m/s 2 1, 400 m/s 2 4 m/s 2 Question

Which of the following are possible units of acceleration? 1. 2. 3. 4. seconds

Which of the following are possible units of acceleration? 1. 2. 3. 4. seconds feet / second 2 Question

Two and Three Dimensional Motion • These examples had motion in only one dimension.

Two and Three Dimensional Motion • These examples had motion in only one dimension. • Two dimensional motion is common also. • An example is a car rounding a corner.

Two and Three Dimensional Motion • Three dimensional motion is not unusual. • An

Two and Three Dimensional Motion • Three dimensional motion is not unusual. • An example is a car rounding a corner on a hill. • This type of motion uses “spatial” dimensions, so called because 3 dimensions enclose a volume or space.

Two and Three Dimensional Motion • A car rounding a corner is changing its

Two and Three Dimensional Motion • A car rounding a corner is changing its direction. • Direction is part of velocity, so the car is accelerating even if its speed is constant.

Two and Three Dimensional Motion When a car repeatedly comes to a stop from

Two and Three Dimensional Motion When a car repeatedly comes to a stop from the same speed—as in a busy downtown with red lights—its acceleration is closer to zero if it takes longer to stop.