Chapter 10 Motion -...

MotionChapter 10

Section 1 Measuring Motion

Section 2 Acceleration

Section 3 Motion and Force

• Skills• Experiment Design

• SI Units and SI unit conversions

• Using graphs

• Scientific Notation and use in calculations

• Significant Digits

• Using and manipulating equations

Section 1 Measuring Motion

Objectives

• Explain the relationship between motion and aframe of reference.

• Relate speed to distance and time.

• Distinguish between speed and velocity.

• Solve problems related to time, displacement,velocity, and acceleration.

Observing Motion

• Motion is an object changing position relative toa reference point.

• Distance measures the total path taken.

• Displacement is the change in the position ofan object.• Displacement must always indicate both

magnitude and direction.

Motion

Distance vs. Displacement

Speed and Velocity

• Speed is the distance traveled divided by thetime interval during which the motion occurred.Speed describes how fast an object moves.

• Speed measurements involve distance and time.

• The SI units for speed are meters per second(m/s).

• When an object covers equal distances in equalamounts of time, it is moving at a constant speed.

Speed

Speed and Velocity, continued

• Speed can be determinedfrom a distance-time graph.

• When an object’s motion isgraphed by plotting distanceon the y-axis and time on

the x-axis, the slope of thegraph is speed.

Speed and Velocity, continued• Average speed is calculated as total distance divided by

total time. (sA)

• Instantaneous speed is the speed at a given point intime. (s)

• Average velocity is calculated as total displacement(change in position) divided by total time. (vA)

• Instantaneous velocity is the velocity at a given point intime. (v)

,t

dv vtd

v

dt

t

xvA

Math Skills

Velocity Metal stakes are sometimes placed inglaciers to help measure a glacier’s movement.For several days in 1936, Alaska’s BlackRapids glacier surged as swiftly as 89 metersper day down the valley. Find the glacier’svelocity in m/s. Remember to include direction.

1. List the given and the unknown values.

Given: time, t = 1 day

displacement, d = 89 m down the valley

Unknown: velocity, v = ? (m/s and direction)

Math Skills, continued

2. Perform any necessary conversions.

To find the velocity in meters per second, the value fortime must be in seconds.

s8.64x1086,400st

min

s60

hr

60min

day

hr24day1t

4

Math Skills, continued

3. Write the equation for velocity.

v =dt =

89 m8.64 104 s

(For velocity, include direction.)

v = 1.0 10–3 m/s down the valley

4. Insert the known values into the equation,and solve.

t

d

time

tdiplacemenvelocity

Speed and Velocity, continued

• Velocity describes both the speed and thedirection of an object.

• Velocities can be combined to determine theresultant velocity.

Speed and Velocity, continued

Velocity

Practice p.323; Math Skills p.324

Section 2 Acceleration

Objectives

• Describe the concept of acceleration as achange in velocity.

• Explain why circular motion is continuousacceleration even when the speed does notchange.

• Calculate acceleration as the rate at whichvelocity changes.

• Graph acceleration on a velocity-time graph.

Which of the following examples shows achange in velocity? Remember a change invelocity can be either a change in speed or achange in the direction of motion.

a. a car coming to a stop at a stop sign

b. a book sitting on a desk

c. a yo-yo in motion

d. a car going around a curve at exactly 80 km/h

Acceleration and Motion

• Acceleration is the rate at which velocitychanges over time.

• An object accelerates if its speed, direction, orboth change.

Acceleration

Calculating Acceleration

• Acceleration is the rate at which velocity changes.

Acceleration Equation (for straight-line motion)

t

vv

time

velocityinitialvelocityfinal

timeinchange

velocityinchangeonaccelerati if

• In SI units, acceleration is measured in meters persecond per second (m/s/s) or m/s2.

t

vaA

Math Skills

Acceleration A flowerpot falls off a second-storywindowsill. The flowerpot starts from rest and hitsthe sidewalk 1.5 s later with a velocity of 14.7m/s. Find the average acceleration of theflowerpot.

1. List the given and the unknown values.

Given: time, t = 1.5 s

initial velocity, vi = 0 m/s

final velocity, vf = 14.7 m/s down

Unknown: acceleration, a = ? (m/s2 and direction)

Math Skills, continued

3. Insert the known values into the equation,and solve.

a =vf – vi

t =14.7 m/s – 0 m/s

1.5 s

a =14.7 m/s

1.5 s = 9.8 m/s2 down

acceleration =final velocity – initial velocity

time =vf – vi

t

2. Write the equation for acceleration.

Calculating Acceleration, continued

Acceleration can bedetermined from avelocity-time graph.

Graphical Representations ofAcceleration

Acceleration and Motion, continued

• Acceleration can be a change in speed.

• Acceleration can be a change in direction.

• Uniform circular motion is constant acceleration.

Centripetal Acceleration

r

va

2

c

Math Skills

Centripetal Acceleration A corvette is going arounda 50m radius curve travelling at 25 m/s (50mph).What is the centripetal acceleration on thepassenger?

1. List the given and the unknown values.

Given: velocity, v = 25 m/s

radius, r = 50 m

Unknown: acceleration, ac = ? (m/s2 and direction)

Math Skills, continued

3. Insert the known values into the equation,and solve.

m50

)s/m25(

r

va

22

c

2. Write the equation for acceleration.

r

va

2

c

222

c s/m5.12m50

s/m625a

Acceleration and Motion, continued

t

vaaA

t

xvA

t

vv

t

vv

t

va

if 0

atvv 0

atvv 0

22, 0vvvv

vt

xv

if

AA

20vv

t

x

2

2

2000 tatvtvatv

x

20

2

1attvx xavv 2

2

02

a

vvt 0

2

0 tvvx

200

2

1attvxx

Acceleration and Motion, continued

t

va

t

xvA

atvv 0

20

2

1attvx

xavv 22

02

Note: a = constant

Practice p.323Practice p.328; Math Skills p.330

Math Skills

Velocity and Acceleration An idiot drops a quarteroff the top of the Empire State Building (h=500m).How far has the coin dropped and what is itsvelocity after 1 s? 2s? 3s? 4s? 5s? How long willit take for the coin to hit the pedestrian below?What will be its velocity? How many years shouldthe idiot spend behind bars?

Math Skills, continued

1. List the given and the unknown values.

Given: height, h = 500 m

(velocity, v0 = 0 m/s)

(acceleration, g = 10 m/s2)

Unknown: @ t = 1,2,3,4,and 5s

distance dropped, Δx = ? (m)

velocity, v = ? (m/s and direction)

impact velocity, vf = ? (m/s)

time of impact, t = ? (s)

time with Bubba, sentence = ? (Years)

Math Skills, continued

3. Insert the known values into the equation,and solve.

2. Write the equations for Δx and velocity.

20 at

2

1tvx atvv 0 xa2vv

2

02

Practice Worksheet 10-1

Section 3 Motion and Force

Objectives

• Explain the effects of unbalanced forces on themotion of objects.

• Compare and contrast static and kineticfriction.

• Describe how friction may be either harmful orhelpful.

• Identify ways in which friction can be reduced orincreased.

Balanced and Unbalanced Forces

• Force is an action exerted on a body in order tochange the body’s state of rest or motion. Forcehas magnitude and direction.• The net force is the combination of all forces

acting on an object.

• Objects subjected to balanced forces either donot move or move at constant velocity.

• An unbalanced force must be present to causeany change in an object’s state of motion or rest.

Force

The Force of Friction

• Friction is a force that opposes motion betweentwo surfaces that are in contact.

• Friction opposes the applied force.

The Force of Friction, continued

The Force of Friction, continued

• Static friction resists the initiation of slidingmotion between two surfaces that are in contactand at rest.

• Kinetic friction opposes the movement of twosurfaces that are in contact and are sliding overeach other.

• Static friction is greater than kinetic friction.• There are many different types of kinetic friction, such

as sliding friction and rolling friction.

• Fluid friction, such as air resistance, also opposesmotion.

Types of Friction

Frictional Forces and Acceleration

Friction and Motion

• Friction can be helpful or harmful.

• Friction is necessary to roll a vehicle or hold anobject.

• However, friction can also cause excessiveheating or wear of moving parts.

• Harmful friction can be reduced.

• Helpful friction can be increased.

Ways to Reduce or Increase Friction

• TERMS TOOLS (equations)

• length (x, l, h) (m)

• mass (m) (kg)

• time (t) (s)

• velocity (v) (m/s)

• acceleration (a) (m/s2)

• force (F) (N=kg m/s2)

Chapter Review p.338; 1-9, 16-21

t

xvA

t

vaA

vtd

20

2

1attvx

atvv 0

xavv 22

02

r

vac

2