chapter 10 motion -...
TRANSCRIPT
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MotionChapter 10
Section 1 Measuring Motion
Section 2 Acceleration
Section 3 Motion and Force
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• Skills• Experiment Design
• SI Units and SI unit conversions
• Using graphs
• Scientific Notation and use in calculations
• Significant Digits
• Using and manipulating equations
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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.
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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.
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Motion
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Distance vs. Displacement
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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.
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Speed
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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.
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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
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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)
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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
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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
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Speed and Velocity, continued
• Velocity describes both the speed and thedirection of an object.
• Velocities can be combined to determine theresultant velocity.
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Speed and Velocity, continued
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Velocity
Practice p.323; Math Skills p.324
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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.
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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
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Acceleration and Motion
• Acceleration is the rate at which velocitychanges over time.
• An object accelerates if its speed, direction, orboth change.
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Acceleration
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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
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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)
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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.
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Calculating Acceleration, continued
Acceleration can bedetermined from avelocity-time graph.
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Graphical Representations ofAcceleration
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Acceleration and Motion, continued
• Acceleration can be a change in speed.
• Acceleration can be a change in direction.
• Uniform circular motion is constant acceleration.
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Centripetal Acceleration
r
va
2
c
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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)
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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
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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
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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
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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?
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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)
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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
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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.
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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.
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Force
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The Force of Friction
• Friction is a force that opposes motion betweentwo surfaces that are in contact.
• Friction opposes the applied force.
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The Force of Friction, continued
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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.
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Types of Friction
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Frictional Forces and Acceleration
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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.
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Ways to Reduce or Increase Friction
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• 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