Physical Physical ScienceScience

Unit: MotionUnit: Motion

Physics:

A branch of Physical science that deals with physical changes of objects.

The models on which Physics is based are most frequently expressed in mathmatical equations that describe the conditions of the real world.

The primary task in studying physics is to understand its basic principles

Motion

Is a change in position relative to a frame of reference

Motion is measured by distance and time.

Frame of reference

The object or point from which movement is determined

Movement can only be measured with reference to something that is assumed to be fixed in place

The most common frame of reference is the Earth

Are You Moving ?Are You Moving ?

You are sitting down, reading a book…. You are sitting down, reading a book…. Are you moving?Are you moving? Object is in motion when its distance from Object is in motion when its distance from

another object is changing.another object is changing. All depends on the “Point of Reference” All depends on the “Point of Reference” Therefore object is in motion if it changes position Therefore object is in motion if it changes position

relative to a reference point.relative to a reference point.

International System of International System of UnitsUnits ““SI” SI”

– Based on the number 10Based on the number 10– Distance (length) uses Distance (length) uses metermeter (about 39 inches) (about 39 inches)– Mass (how much matter) uses Mass (how much matter) uses gramgram ( a nickel is about 5 ( a nickel is about 5

grams)grams)– Volume (how much space)Volume (how much space)

Liquid volume – uses Liquid volume – uses literliter ( a little more than a quart) ( a little more than a quart)

Solid volume – usesSolid volume – uses cm cm33 ( about the size of a sugar cube)( about the size of a sugar cube)

1 ml = 1 cm1 ml = 1 cm33

– Weight (affect gravity has on object) uses Weight (affect gravity has on object) uses newtonnewton ( an ( an apple weighs about 1 newton) (1 pound is about 4.4 apple weighs about 1 newton) (1 pound is about 4.4 newtons)newtons)

– Density = Mass / Volume Density = Mass / Volume = grms / ml= grms / ml

To Amplify the PointTo Amplify the Point Distances can be short or very long.Distances can be short or very long.

– Basic metric unit of length is the meter.Basic metric unit of length is the meter.– Metric prefixes are based on the number 10.Metric prefixes are based on the number 10.– 10 meters = 1 decameter10 meters = 1 decameter– 10 decameters = 1 hectometer10 decameters = 1 hectometer– 10 hectometer = 1 kilometer10 hectometer = 1 kilometer– Therefore : 1 kilometer =1000 metersTherefore : 1 kilometer =1000 meters– And…And…– There are 10 decimeters in a meter There are 10 decimeters in a meter – There are 10 centimeters in a decimeter There are 10 centimeters in a decimeter – There are 10 millimeter in a centimeterThere are 10 millimeter in a centimeter– Therefore: 1000 millimeters = 1 meterTherefore: 1000 millimeters = 1 meter

Metric StairsMetric Stairs You should be comfortable with converting from You should be comfortable with converting from

[cm] [cm] toto [m], [mm] [m], [mm] toto [km], [km], and so on.and so on.

Convert: 1527 centigrams into hectograms: going four steps up means you move the decimal 4 places to the left. Therefore:

1527 centigrams = .1527 hectograms&

9.8712345 kg = (steps to the right) 9871234.5 mg

Graphing ( x,y ) coordinatesGraphing ( x,y ) coordinates A graph w/ points (2,3) , (-2,1) & (1.5, A graph w/ points (2,3) , (-2,1) & (1.5,

-1) plotted: -1) plotted:

Remember: a. the x axis is the horizontal axis

Remember: b. The y axis is vertical axis

c. The origin is (0,0)

More Graphing!More Graphing! Graph the following Graph the following

points:points:a) (3, 3)a) (3, 3)b) (- 2, 3)b) (- 2, 3)c) (- 1, - 2)c) (- 1, - 2)d) (3, 0)d) (3, 0)e) (0, 0)e) (0, 0)f) (0, - 4)f) (0, - 4)

ab

c

de

f

& Still More Graphing….& Still More Graphing…. What are the coordinates of these points?What are the coordinates of these points?

Click for the answers…

a. (2, 0)b) (0, 2) c) (4, 3) d) (-1, 3)e) (-3, 3) f) (-1, -3) g) (-3, -1)h) (2, -4)

Working w/ UnitsWorking w/ Units

Determining the correct units in a Determining the correct units in a problem is just as important as getting problem is just as important as getting the number correct.the number correct.

Remember we can “cancel” numerators Remember we can “cancel” numerators & denominators to make the math & denominators to make the math easier:easier:

24 x 6 x 2 x 9 x 18 24 x 6 x 2 x 9 x 18 = = 24 x 6 x 2 x 9 x 1824 x 6 x 2 x 9 x 18 = 1 = 1

12 x 18 x 3 x 3x 24 12 x 18 x 3 x 3 x 24 12 x 18 x 3 x 3x 24 12 x 18 x 3 x 3 x 24

We can do the same w/ units…. We can do the same w/ units….

Multiplying & Dividing UnitsMultiplying & Dividing Units Do this problem:Do this problem:

5 minutes x 3 feet = 15 minute feet 5 minutes x 3 feet = 15 minute feet Do this problem:Do this problem:

12 miles12 miles 4 4 milesmiles

3 hours hour3 hours hour Do this problem:Do this problem:

mile x week x dollar x bananas x week x newton x week mile x week x dollar x bananas x week x newton x week

dollar x newton x mile x bananas x week x kilogram x week dollar x newton x mile x bananas x week x kilogram x week

mile x week x dollar x bananas x week x newton x weekmile x week x dollar x bananas x week x newton x week week week

dollar x newton x mile x bananas x week x kilogram x week kilometer dollar x newton x mile x bananas x week x kilogram x week kilometer

Speed = distance / timeSpeed = distance / time Formula: S=D/TFormula: S=D/T What is the speed of a car that traveled 75 km in 1.5 What is the speed of a car that traveled 75 km in 1.5

hr?hr? S = D / T = 75km / 1.5 hr = 50 km/hrS = D / T = 75km / 1.5 hr = 50 km/hr

Since distance is measured in meters or Since distance is measured in meters or kilometers and time is measured in seconds kilometers and time is measured in seconds or hours, the units of speed are meters per or hours, the units of speed are meters per second (m/sec) or kilometers per hour (km/hr)second (m/sec) or kilometers per hour (km/hr)

In Physics, distance can be thought of as In Physics, distance can be thought of as having a directions. The distance is called having a directions. The distance is called displacement.displacement.

Graphing AccelerationGraphing Acceleration

You can use both a speed - versus - You can use both a speed - versus - time graph and a distance - versus - time graph and a distance - versus - time graph to analyze the motion of time graph to analyze the motion of an accelerating object.an accelerating object.

Speed - Versus - Time Speed - Versus - Time GraphGraph

The slope of a line on a speed - The slope of a line on a speed - versus - time graph represents versus - time graph represents acceleration.acceleration.

Distance - Versus - Time Distance - Versus - Time GraphGraph

You can also show the motion of an You can also show the motion of an accelerating object with a distance - accelerating object with a distance - versus - time graph.versus - time graph.

Constant Speed

Speed that does not change.

Slope: The slant of a line connecting 2 points that indicates the change in the y axis as compared to the change in the x axis

Graphing line slopes Graphing line slopes (rise/run)(rise/run) 1. Graph the line which passes through (2, 3) and 1. Graph the line which passes through (2, 3) and

has a slope of 2/3.has a slope of 2/3. 2. Graph the line which passes through (1, 1) and 2. Graph the line which passes through (1, 1) and

has a slope of -4. (remember - 4 = -4/1)has a slope of -4. (remember - 4 = -4/1)

1 2

(2,3) (1,1)

Graphing points & slope Graphing points & slope (rise/run)(rise/run) 1. Graph the line which passes through (0, 2) and 1. Graph the line which passes through (0, 2) and

has a slope of 3. has a slope of 3. (remember 3 can be written as 3/1)(remember 3 can be written as 3/1)

2. Graph the line which passes through (- 1, 1) 2. Graph the line which passes through (- 1, 1) and has a slope of – 2/3. and has a slope of – 2/3.

1 2

(0,2)(-1,1)

Notice the difference in the graphs for constant speed and for average speed

Average Speed

The measure of speed obtained by dividing the total distance by the total time.

The speed of a moving objet is not always constant

Speed that changes is not constant speed Dividing the total distance by the total time

gives the average speed NOT the actual speed at that instance

Average Speed or Average Average Speed or Average VelocityVelocity

Average speed = total distance / total timeAverage speed = total distance / total time

What is the average speed after 2 minutes? total distance is 75m, total time is 2 minutes.

S = D/TS = 75m / 2minS= 37.5 m/min

What is the average speed between 2 & 4 minutes? total distance: 110m – 75m = 35m total time: 4min – 2min = 2minutes total time

S = D/TS = 35m / 2minS= 17.5 m/min

Example Problem : Speed

A truck travels to and from a stone quarry that is located 2.5 km to the east. What is its distance? What is its displacement?

Solution:

Distance = 5 km, Displacement = 0 km

Example Problem average acceleration

During a race, a sprinter increases from 5.0 m/s to 7.5 m/s over a period of 1.25 s. What is the sprinter’s average acceleration during this period?

Solution:

(7.5 -5)/ 1.25= 2.0 m/s2

Example Problem average speed

A cross-country runner runs 10 km in 40 minutes. What is his average speed?

Solution:

Average speed = total distance / total timeAverage speed = total distance / total time 10 km/40 min10 km/40 min = = 0.25 km / m0.25 km / m

Example Problem Speed James rode his bike 0.65 hours and traveled 8.45

km. What was his speed?

Solution:

Speed = distance /time

0.65 hr = t 8.45 km = d s = d/t s = 8.45/0.65 s = 13 km/hr

Example Problem Speed Brittany drove at a speed of 85 km / hr south for

4 hours. How far did she travel?

Solution:

Speed = distance/ time

85 km / hr = s 4 hrs = t ? = d s = d/t 85 km/hr = d / 4 hrs d = 340 km

Example Problem Velocity A dog travels 250 meters east in 8

seconds. What is the velocity of the dog?

Solution:

250 m = d 8 s = t ? = v v = d/t v = 250 / 8 v = 2.5 ,/s

Example Problem Acceleration

8. A runner went from 6 m/s to 2 m/s in 2 seconds, what was his acceleration?

Solution:

6 m/s = vi2 m/s = vf2 s = t? = aa = vf - vi / ta = 2 – 6 / 2a = -2 m/s2

Example Problem Speed

A high speed train travels with an average speed of 227 km/h. The train travels for 2 h. How far does the train travel?

Solution:

d = s ´ t = 227 km/h ´ (2.00 h) = 454 km

Example Problem Speed

A dog travels north for 18 meters, east for 8 meters, south for 27 meters and then west for 8 meters. What is the distance the dog traveled and what is the displacement of the dog

Solution:

distance = 61 m displacement = 9 meters south

Example problem The driver of a pickup truck drove at a velocity of

75.0 km/m for 33 minutes. What distance did the bus travel?

Solution:

75 km / m = v 33 m = t ?= d v = d/t d = 75 x 33 d = 2475 km

VelocityVelocity

Velocity is speed with a directionVelocity is speed with a direction

Written like: Written like: 125 miles/hour east 125 miles/hour east or or 83 m/sec towards the 83 m/sec towards the househouse

What is the velocity of a jet that traveled 1623 mi North in 83 min?What is the velocity of a jet that traveled 1623 mi North in 83 min?

V = D / T = 1623 mi / 83 min = 19.5 mi/min NorthV = D / T = 1623 mi / 83 min = 19.5 mi/min North

Velocity

The velocities that have the same direction combine by addition:

Ex you are rowing downstream at 6 km/hr and the velocity of the river is 10 km/hr. You are actually moving at 16 km/hr

Velocity

Velocities that have opposite directions combine by subtraction

Ex You are rowing upstream at 10km/hr and the velocity of the river is 8km/hr. You are acturally moving at 2km/hr

Velocity

This idea is important in launching rockets

Rockets are launched in the same direction as the earth rotates ( about 1800 km/hr)

Thus the rocket engines and the Earth’s rotational speed work together to break the Earth’s gravitational force

AccelerationAcceleration The change in speed or velocity over timeThe change in speed or velocity over time

– In scientific community, the symbol for In scientific community, the symbol for “change” is the triangle:“change” is the triangle:

– Change in velocity is found by subtracting the Change in velocity is found by subtracting the final speed from the initial speedfinal speed from the initial speed

VVff - V - Vii = V = V

The formula for acceleration is:The formula for acceleration is:

A = A = VVff - V - Vii = V = V

time timetime time

Therefore the units for acceleration are going to be a

distance/time/time

Example

ft/min/sec

AccelerationAcceleration For an object to accelerated it must:For an object to accelerated it must:

– Speed up (Speed up (positive accelerationpositive acceleration))– Slow down (Slow down (negative accelerationnegative acceleration a.k.a deceleration ) a.k.a deceleration )– Change direction of travelChange direction of travel

Each of these pictures depicts a type of acceleration:1: the shuttle is speeding up every sec of the flight into

orbit2. the horse has come to a screeching halt (slowing down)3. the baseball thrown to the batter is hit into the outfield

(changed direction)

12

3

What’s it mean?What’s it mean? What does a = 5 [m/secWhat does a = 5 [m/sec22] mean?] mean? If an object starts at rest, its If an object starts at rest, its velocityvelocity

increases by 5 [m/sec] increases by 5 [m/sec] every second.every second.

Time (sec) Acceleration Velocity

0 5 m/sec2 0 m/sec

1 5 m/sec2 5 m/sec

2 5 m/sec2 10 m/sec

3 5 m/sec2 15 m/sec

4 5 m/sec2 20 m/sec

Therefore, an object accelerating at 5m/sec2 will be travelling at 20 m/sec after 4 seconds.

Acceleration Problems:Acceleration Problems:

Calculate acceleration for the following data:Calculate acceleration for the following data:

A = 60km/hr - 20 km/hr = 4 km/hr 10 sec sec

A = 150km/sec - 50 km/sec = 20 km 5 sec sec2

A = 1200km/hr - 25 km/hr = 587.5 km/hr 2 min min

Circular Motion

Acceleration is a change in velocity Remember velocity expresses

direction as well as speed An object in circular motion is

accelerating even though its speed may be constant

Acceleration that is directed toward the center of a circular path is called centripetal acceleration

Centripetal Acceleration

Momentum

All moving objects have momentum Momentum is equal o the mass of an

object multiplied by its velocity.

Momentum = mass x velocity

Momentum

An objects momentum depends on both its mass and velocity

Ex stopping distance of a car is directly related to its momentum ( how fast it is moving and the mass of the car)

Momentum Momentum Momentum = mass x velocity Momentum = mass x velocity For some reason, maybe because mass is For some reason, maybe because mass is

designated as “m” in formulas, momentum is designated as “m” in formulas, momentum is designated as “designated as “pp”. ”.

Therefore: Therefore: pp = mv = mv The unit for The unit for mass is kgmass is kg, the unit for , the unit for velocity is velocity is

meter/secondmeter/second, therefore the unit for , therefore the unit for momentum is momentum is kg m/seckg m/sec

Conservation of MomentumConservation of Momentum::– When two or more objects interact (collide) the total When two or more objects interact (collide) the total

momentum before the collision is equal to the total momentum before the collision is equal to the total momentum after the collisionmomentum after the collision

Momentum – 2 moving Momentum – 2 moving objectsobjects During this collision the speed of both box cars During this collision the speed of both box cars

changes. The total momentum remains constant changes. The total momentum remains constant before & after the collision. The masses of both cars before & after the collision. The masses of both cars is the same so the velocity of the red car is is the same so the velocity of the red car is transferred to the blue car.transferred to the blue car.

Momentum – 1 moving Momentum – 1 moving objectobject During this collision the speed red car is transferred During this collision the speed red car is transferred

to the blue car. The total momentum remains to the blue car. The total momentum remains constant before & after the collision. The masses of constant before & after the collision. The masses of both cars is the same so the velocity of the red car is both cars is the same so the velocity of the red car is transferred to the blue car.transferred to the blue car.

Momentum – 2 connected Momentum – 2 connected objectsobjects After this collision, the coupled cars make one object After this collision, the coupled cars make one object

w/ a total mass of 60,000 kg. Since the momentum w/ a total mass of 60,000 kg. Since the momentum after the collision must equal the momentum before, after the collision must equal the momentum before, the velocity must change. In this case the velocity is the velocity must change. In this case the velocity is reduced from 10 m/sec. to 5 m/sec. reduced from 10 m/sec. to 5 m/sec.

Example problems: Momentum

A motorcycle has a mass of 250 kg and a velocity of 68 m/s, what is it’s momentum?

Solution:

Momentum = mass x velocity

250 kg x 68 m/s = 17000kg m/s

Example problems: Momentum

A 10-kg wagon has a speed of 25 m/s. What is its momentum?

Solution:

10 kg x 25 m/s = 250 kg m/s

Momentum = mass x velocity

Example problems: Momentum

A 10.0 kg dog chasing a rabbit north at 6.0 m/s has a momentum of?

Solution: Momentum = mass x velocity 10kg x 6 m/s = 60 kgm/s

Example Problem Momentum

A large truck loaded with scrap steel weighs 14 metric tons and is traveling north on the interstate heading for Chicago. It has been averaging 48 hm/h for the journey and has traveled over 1450 km so far. It has just stopped to refuel. What is its current momentum?

Solution:

0 (zero) kg•m/s Remember it is not moving

Example Problem Momentum

How fast is a car traveling if it has a mass of 2200kg and a momentum of 28000 kgm/s?

Solution (answer 12.72 m/s)

Law of conservation of momentum

The total momentum of any object or group of objects remains the same unless outside forces act on the object.

ScientistScientist

Modern scientist understand the Modern scientist understand the relationships between force and relationships between force and motion, motion,

However it took over 2000 years to However it took over 2000 years to figure it outfigure it out

Aristotle:Aristotle:

Inaccurately proposed that force is Inaccurately proposed that force is required to keep an object moving at required to keep an object moving at constant speedconstant speed

This slowed down the study of This slowed down the study of motion for nearly 2000 yearsmotion for nearly 2000 years

GalileoGalileo

Proved thru observations that the Proved thru observations that the Earth is one of many planets, all Earth is one of many planets, all governed by the same laws of governed by the same laws of Gravity Gravity

Concluded that objects not subjected Concluded that objects not subjected to friction or any other force would to friction or any other force would continue to move indefinitely continue to move indefinitely

Isaac NewtonIsaac Newton

Built on Galileo’s work and developed Built on Galileo’s work and developed the 3 laws of motionthe 3 laws of motion