physics beyond 2000 chapter 1 kinematics physical quantities fundamental quantities derived...
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Physics Beyond 2000
Chapter 1
Kinematics
Physical Quantities
• Fundamental quantities
• Derived quantities
Fundamental QuantitiesQuantity Symbol SI Unit
Mass m kg
Length l m
Time t s
Others - -
http://www.bipm.fr/
Derived Quantities
• Can be expressed in terms of the basic quantities
• Examples– Velocity– Example 1– Any suggestions?
Derived Quantities
• More examples
Standard Prefixes
• Use prefixes for large and small numbers
• Table 1-3
• Commonly used prefixes– giga, mega, kilo– centi, milli, micro, nana, pico
Significant Figures
• The leftmost non-zero digit is the most significant figure.
• If there is no decimal point, the rightmost non-zero digit will be the least significant figure.
• If there is a decimal point, the rightmost digit is always the least significant figure.
The number of digits between the Most significant figure and least significant figure inclusive.
Scientific Notation
• Can indicate the number of significant numbers
Significant Figures
• Examples 5 and 6.
• See if you understand them.
Significant Figures
• Multiplication or division.– The least number of significant figures.
• Addition or subtraction.– The smallest number of significant digits on the
right side of the decimal point.
Order of Magnitude
• Table 1-4.
Measurement
• Length– Meter rule– Vernier caliper– Micrometer screw gauge
Practice
Measurement
• Time interval– Stop watch– Ticker tape timer– Timer scaler
Measurement
• Mass– Triple beam balance– Electronic balance
Measurement
• Computer data logging
Error Treatment
• Personal errors– Personal bias
• Random errors– Poor sensitivity of the apparatus
• System errors– Measuring instruments – Techniques
Accuracy and Precision
• Accuracy– How close the measurement to the true value
Precision– Agreement among repeated
measurements– Largest probable error tells the precision
of the measurement
Accuracy and Precision
• Examples 9 and 10
Accuracy and Precision
• Sum and difference– The largest probable error is the sum of the
probable errors of all the quantities.– Example 11
Accuracy and Precision
• Product, quotient and power– Derivatives needed
Kinematics
• Distance d
• Displacement s
Average Velocity
• Average velocity
= displacement time taken
t
svav
Instantaneous Velocity
• Rate of change of displacement in a very short time interval.
dt
sd
t
sv
t
)(lim0
Uniform Velocity
• Average velocity = Instantaneous velocity when the velocity is uniform.
Speed
• Average speed
t
dSpeedav
• Instantaneous speed
t
dSpeed
t
lim0
Speed and Velocity
• Example 13
Relative Velocity
• The velocity of A relative to BBAAB vvv
ABBA vvv
• The velocity of B relative to A
Relative Velocity
• Example 14
Acceleration
• Average acceleration
• Instantaneous acceleration
Average acceleration
• Average acceleration =
change in velocity time
t
vaav
Example 15
Instantaneous acceleration
dt
vd
t
va
t
)(lim0
Example 16
Velocity-time graphv-t graphv
t
Slope: = accelerationdt
dv
v-t graph
• Uniform velocity: slope = 0v
t
v-t graph
• Uniform acceleration: slope = constant
v
t
Falling in viscous liquid
Acceleration
Uniform velocity
Falling in viscous liquid
v
tacceleration:slope=g at t=0
uniform speed:slope = 0
Bouncing ball with energy loss
Falling: with uniform acceleration a = -g.
Let upward vector quantities be positive.
v-t graph of a bouncing ball
• Uniform acceleration: slope = -g
v
t
falling
Bouncing ball with energy loss
Rebound: with large acceleration a.
Let upward vector quantities be positive.
v-t graph of a bouncing ball
• Large acceleration on rebound
v
t
falling
rebound
Bouncing ball with energy loss
Rising: with uniform acceleration a = -g.
Let upward vector quantities be positive.
v-t graph of a bouncing ball
• Uniform acceleration: slope = -g
v
t
falling
reboundrising
v-t graph of a bouncing ball• falling and rising have the same acceleration:
slope = -g
v
t
falling
reboundrising
The speed is less after rebound
Linear Motion: Motion along a straight line
• Uniformly accelerated motion: a = constant
velocity
time
v
u
t0
v
Uniformly accelerated motion
• u = initial velocity (velocity at time = 0).
• v = final velocity (velocity at time = t).
• a = acceleration
t
uv
t
va
v = u + at
Uniformly accelerated motion
• = average velocityv )(2
1vu
time
v
u
t0
v
velocity
Uniformly accelerated motion
time
v
u
t0
v
velocity
s = displacement = tvutv )(2
1
s = area below the graph
Equations of uniformly accelerated motion
tvus
asuv
atuts
atuv
)(2
1
2
2
1
22
2
Uniformly accelerated motion
• Example 17
Free falling: uniformly accelerated motion
Let downward vector quantities be negative
a = -g
Free falling: uniformly accelerated motion
tvus
gsuv
gtuts
gtuv
)(2
1
2
2
1
22
2
a = -g
Free falling: uniformly accelerated motion
Example 18
Parabolic Motion
• Two dimensional motion under constant acceleration.
• There is acceleration perpendicular to the initial velocity
• Examples:– Projectile motion under gravity.– Electron moves into a uniform electric field.
Monkey and Hunter Experiment
gun
bullet aluminiumfoil
electromagnet
iron ball
Monkey and Hunter Experiment
gun
bullet aluminiumfoil
electromagnet
iron ball
The bullet breaks the aluminium foil.
Monkey and Hunter Experiment
gun
bullet
electromagnet
iron ball
Bullet moves under gravity.Iron ball begins to drop.
Monkey and Hunter Experiment
gun
bullet
electromagnet
Bullet is moving under gravity.Iron ball is dropping under gravity.
Monkey and Hunter Experiment
gun
electromagnet
Monkey and Hunter Experiment
gun
electromagnet
The bullet hits the ball!
Monkey and Hunter Experiment
• The vertical motions of both the bullet and the iron are the same.
• The vertical motion of the bullet is independent of its horizontal motion.
Projectile trajectoryy
x
Projectile trajectoryy
x
Projectile trajectoryy
x
u
u = initial velocity = initial angle of inclination
Projectile trajectoryy
x
u
v = velocity at time t = angle of velocity to the horizontal at time t
v
Horizontal line
Projectile trajectoryy
x
u
xu
yu
= x-component of u = y-component of uyuxu
Projectile trajectoryy
x
u
xu
yu
sin.
cos.
uu
uu
y
x
Projectile trajectory:accelerationsy
x
u
xu
yu
ga
a
y
x
0
Projectile trajectoryy
x
u
v
Horizontal line
xu
yuvertical line
xvyv
= x-component of v = y-component of vxvyv
Projectile trajectory: velocity in horizontal directiony
x
u
v
Horizontal line
xu
yu
xv
cos.uuv xx 0xa
Projectile trajectory:velocity in vertical directiony
x
u
v
yuvertical line
yv
tgutguv
ga
yy
y
.sin..
Horizontal line
Projectile trajectory:displacement
y
x x = x-component of s y = y-component of s
s
s = displacement
Projectile trajectory:horizontal displacement
y
x
s
s = displacement
cos..0 uttuxa xx
Projectile trajectory:vertical displacement
y
x
s
s = displacement
22
2
1sin.
2
1gtutgttuy
ga
y
y
Equation of trajectory:a parabolic path
y
x
s
s = displacement
222
.cos2
tan. xu
gxy
Projectile trajectory:direction of motiony
x
u
v
Horizontal line
xu
yuvertical line
xvyv
Angle represents the direction of motion at time t.
Projectile trajectory:direction of motiony
x
u
v
Horizontal line
xu
yuvertical line
xvyv
cos.
sin.tan
u
gtu
v
v
x
y
Projectile trajectory
• Example 19
Projectile trajectory: maximum height H
y
x
u
H
At H, = 0yv g
uH
2
sin 22
Projectile trajectory: range R
y
x
u
At R, y = 0
R
g
uR
2sin2
Projectile trajectory: maximum range Rmax
y
x
u
Rmax
g
uR
2sin2
is maximum when o902
Projectile trajectory: maximum range Rmax
y
x
u
Rmax
R is maximum when o45
Projectile trajectory: maximum range Rmax
y
x
u
Rmax
g
uR
2
max
Projectile trajectory: time of flight to
y
x
u
At time= to , y = 0
R to
g
uto
sin2
Projectile trajectory: two angles for one range
y
x1 R
2
uu
1= - 2o90