Physics of Motion. Frame of Reference- background or object that shows a change in position. Ex....
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Transcript of Physics of Motion. Frame of Reference- background or object that shows a change in position. Ex....
Physics of MotionPhysics of Motion
Frame of Reference- background or Frame of Reference- background or object that shows a change in object that shows a change in position.position.
Ex. Earth or the HorizonEx. Earth or the Horizon
Fixed in place. If an object is moved Fixed in place. If an object is moved from here we have had some kind of from here we have had some kind of motion.motion.
What is the difference between speed and acceleration?
Can a car be speeding very fast and have zero acceleration?
SpeedSpeed
Speed is a measure of how much Speed is a measure of how much distance is covered in a given distance is covered in a given amount of time.amount of time.
It’s one example of a It’s one example of a rate.rate. Speed is a distance divided by a timeSpeed is a distance divided by a time
S = D/ TS = D/ T
UNITSUNITS
Any distance unit Any distance unit and any time unit and any time unit can be used to can be used to define a speeddefine a speed
Examples km/hr, Examples km/hr, meters/sec, mi/hr,meters/sec, mi/hr,
cm/sec, light cm/sec, light years/century etc.years/century etc.
Comparing UnitsComparing Units
20 km/h20 km/h 12 mi/h12 mi/h 6 m/s6 m/s
40 km/h40 km/h 25 mi/h25 mi/h 11 m/s11 m/s
60 km/h60 km/h 37 mi/h37 mi/h 17 m/s17 m/s
80 km/h80 km/h 50 mi/h50 mi/h 22 m/s22 m/s
100 km/h100 km/h 62 mi/h62 mi/h 28 m/s28 m/s
120 km/h120 km/h 75 mi/h75 mi/h 33 m/s33 m/s
200 km/h200 km/h ?? ??
Comparing UnitsComparing Units
20 km/h20 km/h 12 mi/h12 mi/h 6 m/s6 m/s
40 km/h40 km/h 25 mi/h25 mi/h 11 m/s11 m/s
60 km/h60 km/h 37 mi/h37 mi/h 17 m/s17 m/s
80 km/h80 km/h 50 mi/h50 mi/h 22 m/s22 m/s
100 km/h100 km/h 62 mi/h62 mi/h 28 m/s28 m/s
120 km/h120 km/h 75 mi/h75 mi/h 33 m/s33 m/s
200 km/h200 km/h 120 mi/h120 mi/h ??
Comparing UnitsComparing Units
20 km/h20 km/h 12 mi/h12 mi/h 6 m/s6 m/s
40 km/h40 km/h 25 mi/h25 mi/h 11 m/s11 m/s
60 km/h60 km/h 37 mi/h37 mi/h 17 m/s17 m/s
80 km/h80 km/h 50 mi/h50 mi/h 22 m/s22 m/s
100 km/h100 km/h 62 mi/h62 mi/h 28 m/s28 m/s
120 km/h120 km/h 75 mi/h75 mi/h 33 m/s33 m/s
200 km/h200 km/h 120 mi/h120 mi/h 60 m/s60 m/s
Check for Understanding
On your team’s whiteboard, write an equation and solve for the average speed when Betty swims 50.0 meters in 27.4 seconds. Be sure to use correct units and state your answer in two or three significant figures.
S = D/T = 50.0m/27.4 s = 1.82 m/s
Car Trip
D = 1.22 m T = 1.13 s 1.37 s Use T = 1.25s S = D/T = 1.22m / 1.25 s = 0.976
m/s = 0.98 m/s = 1.0 m/s
Instantaneous vs. Average Speed Instantaneous vs. Average Speed vs. Constant Speedvs. Constant Speed
Instantaneous speed is speed at a Instantaneous speed is speed at a particular instantparticular instant
Constant speed never changesConstant speed never changes Average speed is total distance Average speed is total distance
covered for a trip divided by total covered for a trip divided by total time elapsedtime elapsed
average speed = total average speed = total distance/timedistance/time
Check for UnderstandingCheck for Understanding
What is the difference between What is the difference between instantaneous and average speed?instantaneous and average speed?
ExamplesExamples
Find the average speed of a car trip Find the average speed of a car trip covering 480 km in 6.0 hrs (be sure covering 480 km in 6.0 hrs (be sure to write the symbolic equation first)to write the symbolic equation first)
S = distance/time = D/T = S = distance/time = D/T =
480 km/ 6.0 h = 80. km/h (note that 480 km/ 6.0 h = 80. km/h (note that it’s two significant figures)it’s two significant figures)
Memory TrickMemory Trick
D = S x TD = S x T
S = D/TS = D/T
T = D/ST = D/S
D
S TWhen solving problems, always write the symbolic equation first
Remember your AlgebraRemember your Algebra
S = D/T ; multiply both sides by TS = D/T ; multiply both sides by T S x T = DS x T = D D = S x T; divide both sides by SD = S x T; divide both sides by S D/S = TD/S = T T = D/ST = D/S
When solving problems, always write the symbolic equation first. Then an equal sign, then put in the known numbers, then solve.
Distance UnknownDistance Unknown
Find the distance covered by a horse Find the distance covered by a horse running 18 m/s for one minuterunning 18 m/s for one minute
D = S D = S xx T=18 m/s T=18 m/s x x 60 sec60 sec =1080 m =1080 m Try another one; How far can Sarah run if Try another one; How far can Sarah run if
she averages 4.5 m/s for three minutes she averages 4.5 m/s for three minutes and 20 seconds? (What are we going to and 20 seconds? (What are we going to write first?)write first?)
D = S D = S xx T = 4.5 m/s T = 4.5 m/s x x 3.0 min 3.0 min x x 60s/ 60s/ 1minute = 810 m1minute = 810 m
QuestionQuestion
How long does it take a snail How long does it take a snail creeping at 1.0 cm per second to creeping at 1.0 cm per second to cross a 2.0 meter walkway?cross a 2.0 meter walkway?
T = D/ST = D/S T = 200 cm/ 1.0 cm/sT = 200 cm/ 1.0 cm/s T = 200 sT = 200 s T = 3 minutes 20 seconds T = 3 minutes 20 seconds
Word Problem PracticeWord Problem Practice
Write a symbolic equation for this Write a symbolic equation for this sentence:sentence:
How long does it take for the How long does it take for the Metroliner train to go from NY to Metroliner train to go from NY to Boston, which are 520 km apart, if it Boston, which are 520 km apart, if it averages 127 km/hr?averages 127 km/hr?
Now write in the numbersNow write in the numbers
Now find the answerNow find the answer
Check for understandingCheck for understanding
Does a speedometer measure Does a speedometer measure average speed or instantaneous average speed or instantaneous speed?speed?
Courtesy of CobraCountry.com
Unit ConversionUnit Conversion
Suppose we want to convert 25 m/s Suppose we want to convert 25 m/s to km/hourto km/hour
25 m/s x 1 km/1000m x 3600s/1 hour 25 m/s x 1 km/1000m x 3600s/1 hour = =
This is called the factor-label methodThis is called the factor-label method
90 km/hr
You Try ItYou Try It
Convert 125.0 km/hr to meters/secConvert 125.0 km/hr to meters/sec 125.0 km/hr x 1000m/1 km x 1 125.0 km/hr x 1000m/1 km x 1
hr/3600 sec = hr/3600 sec =
Another word for the “labels” in this Another word for the “labels” in this method would be the ???method would be the ???
34.7 m/s
VelocityVelocity Velocity is speed in a Velocity is speed in a
given directiongiven direction Constant velocity Constant velocity
requires requires bothboth constant constant speed and constant speed and constant directiondirection
Is a car traveling on a Is a car traveling on a circular track at circular track at steady speed moving steady speed moving at constant velocity?at constant velocity?
NO! It’s direction is NO! It’s direction is continually changing.continually changing.
AccelerationAcceleration
How fast How fast velocityvelocity changes changes Acceleration = change of velocity/timeAcceleration = change of velocity/time Includes increases and decreases of Includes increases and decreases of
speed and changes in directionspeed and changes in direction Acceleration (+) Deceleration (-)Acceleration (+) Deceleration (-) a= Vf- Vi/ ta= Vf- Vi/ t Acceleration = a Time = tAcceleration = a Time = t Vf = Final Velocity Vi= Initial VelocityVf = Final Velocity Vi= Initial Velocity
Acceleration EquationsAcceleration Equations
a= Vf-Vi/ta= Vf-Vi/t t = Vf-Vi/at = Vf-Vi/a Vf = (a x t) + ViVf = (a x t) + Vi Vi = Vf – (a x t)Vi = Vf – (a x t)
UNITS MUST MATCH!UNITS MUST MATCH!
Finding AccelerationFinding Acceleration
A car steadily increases its speed A car steadily increases its speed each second from 35 to 40 to 45 each second from 35 to 40 to 45 km/h. What is its acceleration?km/h. What is its acceleration?
Answer: 5 km/h/sAnswer: 5 km/h/s In 10 seconds a train increases speed In 10 seconds a train increases speed
from 20 km/h to 40 km/h. What is its from 20 km/h to 40 km/h. What is its acceleration?acceleration?
a = 20km/h a = 20km/h ÷ 10s = 2.0 km/h/s÷ 10s = 2.0 km/h/s
Free FallFree Fall
In free fall an In free fall an object’s speed object’s speed increases by about increases by about 10 m/s in each 10 m/s in each second. second.
v = gt = 9.8tv = gt = 9.8t
g = 9.8 m/s/sg = 9.8 m/s/s g = 9.8 m/sg = 9.8 m/s22
Time to Time to fall(s)fall(s)
Speed Speed (m/s)(m/s)
00 00
11 9.89.8
22 19.619.6
33 29.429.4
44 39.239.2
55 4949
More on Free FallMore on Free Fall
Due to gravity a = 9.8 m/sDue to gravity a = 9.8 m/s22= g= g v = gtv = gt Instantaneous speed = acceleration Instantaneous speed = acceleration
x timex time Question: What is the speed of a Question: What is the speed of a
rock that has fallen from rest for 5.5 rock that has fallen from rest for 5.5 seconds? (without air resistance)seconds? (without air resistance)
Galileo’s ExperimentGalileo’s Experiment
Which would reach Which would reach the ground first, a the ground first, a marble or a marble or a cannonball?cannonball?
Courtesy Dan Heller Photography
Rising and Falling RockRising and Falling Rock
A rock is thrown upward with 20 m/s. A rock is thrown upward with 20 m/s. It rises then falls to the height from It rises then falls to the height from which thrown. What will be its speed which thrown. What will be its speed at that height? It’s velocity?at that height? It’s velocity?
Answer 20 m/s (down)Answer 20 m/s (down)
Gravity takes speed away on the way up at 9.8 m/s/s and then gives it back on the way down, at the same rate
Distance FallenDistance Fallen
What is average speed of an object that What is average speed of an object that falls for 1 second? falls for 1 second?
What is distance fallen in this time?What is distance fallen in this time?
What is average speed during second What is average speed during second second of fall? second of fall?
What is distance fallen in second second?What is distance fallen in second second?
What is distance fallen in first two What is distance fallen in first two seconds?seconds?
5 m/s, average of 0 and 10
5m = 5 m/s x 1s
15 m/s, average of 10 and 20
15m = 15m/s x 1s
20m = 5m + 15m
The PatternThe Pattern
Distance fallen in t Distance fallen in t secondsseconds
d = 1/2gtd = 1/2gt22
Now if the object is in Now if the object is in motion, then you have motion, then you have to account for that as to account for that as well. well.
d= vd= viit + 1/2gtt + 1/2gt22
timetime distancedistance
11 55
22 2020
33 4545
44 8080
55 125125
Falling AppleFalling Apple
An apple drops from the tree and hits An apple drops from the tree and hits the ground in two secondsthe ground in two seconds
What is its speed when it hits? What is its speed when it hits? What is its average speed?What is its average speed? How high did it fall from?How high did it fall from?
Free Fall ProblemFree Fall Problem
A person is standing on top of a roof, A person is standing on top of a roof, holding two objects. The person drops holding two objects. The person drops item A and at the same time throws item A and at the same time throws item b straight up over the edge of the item b straight up over the edge of the building with an initial speed of 25 m/s. building with an initial speed of 25 m/s. If the building itself is 450 m high, how If the building itself is 450 m high, how long will it take both objects to hit the long will it take both objects to hit the ground and at what speed will they hit ground and at what speed will they hit the ground with?the ground with?
Helicopter ProblemsHelicopter Problems 1. A Helicopter is rising 5.0 m/s and 1. A Helicopter is rising 5.0 m/s and
someone drops a bag from it. After someone drops a bag from it. After two seconds, what is the bags two seconds, what is the bags velocity, how far has the bag fallen velocity, how far has the bag fallen and how far below the helicopter is and how far below the helicopter is the bag?the bag?
2. The helicopter in problem one 2. The helicopter in problem one now descends 5.0 m/s. After two now descends 5.0 m/s. After two seconds, what is the bags velocity, seconds, what is the bags velocity, how far has the bag fallen and how how far has the bag fallen and how far below the helicopter is the bag?far below the helicopter is the bag?
Weather Balloon ProblemWeather Balloon Problem
A weather balloon is floating upward A weather balloon is floating upward at 2.5 m/s above the Earth when it at 2.5 m/s above the Earth when it releases a pack of instruments.releases a pack of instruments.
A. If the pack hits the ground with a A. If the pack hits the ground with a velocity of 73.5 m/s how far did the velocity of 73.5 m/s how far did the pack fall?pack fall?
B. How long did it take for the pack B. How long did it take for the pack to fall?to fall?
Air ResistanceAir Resistance
Why, on earth, Why, on earth, does a coin reach does a coin reach the ground faster the ground faster than a feather?than a feather?
What would What would happen on the happen on the moon?moon?
Confused?Confused?
Explain the difference between velocity Explain the difference between velocity and acceleration and velocity?and acceleration and velocity?
Is acceleration an example of a velocity?Is acceleration an example of a velocity? Can an object with zero velocity be Can an object with zero velocity be
accelerating?accelerating? At the top of its path, the velocity of a rock At the top of its path, the velocity of a rock
thrown upward is ________?thrown upward is ________? At the top, its acceleration is _______?At the top, its acceleration is _______?