Transcript Electric Potential - McMaster Physics and Astronomy

Today’s Lecture…
… will start at 10:30am (and end at regular time)
Physics 1B03summer-Lecture
Day of Wrath
Tuesday June 16
9:30 am – 11:30 am
CNH-104
30 MC Questions, Cumulative
Physics 1B03summer-Lecture
Wave Motion
•Energy and power in sinusoidal waves
Physics 1B03summer-Lecture
Energy in Waves
- as waves propagate through a medium, they
transport energy
eg: ship moving up and down on a lake
eg: feeling sound waves at a rock concert
- hence, we can talk about energy and the
‘rate of energy transfer’
Physics 1B03summer-Lecture
Energy and Power
Energy,Power (amplitude)
2
A stretched rope has energy/unit length:
ds
dm
dx
For small A and large l, we can ignore the
difference between “ds”, “dx” :
dm = μ dx (μ = mass/unit length)
Physics 1B03summer-Lecture
The mass dm vibrates in simple harmonic motion. Its maximum
kinetic energy is
dKmax = ½(dm)vmax2
= ½(dm)(ωA)2
The average kinetic energy is half this maximum value, but
there is also an equal amount of potential energy in the wave.
The total energy (kinetic plus potential) is therefore:
dE = ½(dm) ω 2A2
To get the energy per unit length (or energy ‘density’), replace
the mass dm with the mass per unit length :
E
1
  2 A2
(unit length) 2
Physics 1B03summer-Lecture
Power: Energy travels at the wave speed v,
So
 Energy 
  v
P  
 length 
waves on a string,
P   A v
1
2
2
2
Both the energy density and the power transmitted
are proportional to the square of the amplitude.
This is a general property of sinusoidal waves.
Physics 1B03summer-Lecture
Example
A string for which μ=5.0x10-2 kg/m is under tension of 80.0
N. How much power must be supplied to the string to
generate sinusoidal waves at a frequency of 60Hz and with
an amplitude of 6.0 cm ?
Physics 1B03summer-Lecture
Example
A sinusoidal wave on a string is described by the equation:
y(x,t) = (0.15m)sin(0.80x-50t)
where x is in meters and t in seconds. If μ=12.0g/m,
determine:
a)
b)
c)
d)
e)
the speed of the wave
the speed of particles on the wave at any time
the wavelength
the frequency
the power transmitted to the wave
Physics 1B03summer-Lecture
Quiz
The sound waves from your 100-watt stereo
causes windows across the street to vibrate with
an amplitude of 1 mm. If you use a 400-watt
amplifier, what sort of amplitude can you get from
the windows?
A) 2mm
B) 4mm
C) 16 mm
Physics 1B03summer-Lecture
Intensity
I = Power per unit area
Unit: W / m2
(the area is measured
perpendicular to the
wave velocity)
Intensity ~ (amplitude)2
detectors (area A)
source
Physics 1B03summer-Lecture
Question
How would the intensity depend on distance from
the source for:
1) waves spreading out equally in all directions in
space? (This is called an“isotropic” source, or a
source of “spherical waves”.)
2) Waves spreading out on a two-dimensional
surface, e.g., circular ripples from a stone
dropped into water?
How would the amplitude depend on distance?
Physics 1B03summer-Lecture
10 min rest
Physics 1B03summer-Lecture
Fluid Mechanics and Dynamics
• Pressure
• Pascal’s Law
• Buoyancy
• Bernoulli’s Equation (Fluid Dynamics)
Physics 1B03summer-Lecture
Fluids
- Includes liquids and gases. No resistance to “shear”
(changes in shape), in equilibrium.
- To describe mechanics of a continous fluid (instead
of a discrete object), we use density, pressure
instead of mass and force.
- Dynamics is approached from an energy perspective
(Bernoulli’s equation—next lecture) .
Physics 1B03summer-Lecture
Density
Density, r (“rho”), is mass per unit volume (kg/m3).
Specific Gravity (“SG”) is the ratio:
(density of substance)/(density of water),
which is a pure number (no units).
Substance
water
mercury
air
helium
r
1000 kg/m3
13600 kg/m3
1.29 kg/m3
0.18 kg/m3
SG
1
13.6
0.00129
0.00018
Physics 1B03summer-Lecture
Pressure
P  force per unit area
unit: 1 N/m2 = 1 pascal (Pa)
Also, 1 atmosphere (atm) = 101.3 kPa
Pressure is a scalar property of the
fluid; the force is always exerted
perpendicular to the surface in
contact with the fluid.
Forces exerted
by the fluid
Physics 1B03summer-Lecture
Pascal’s Law: Pressure in an enclosed fluid in
equilibrium is the same everywhere, except for
differences due to gravity.
Or, pressure changes are transmitted throughout a fluid in
equilibrium without loss; there is no static friction in fluids.
push
here
Pressure increases
here as well
Physics 1B03summer-Lecture
Example: How hard do you need to push to lift a
cement truck (weight W = 200 kN)?
w
F1 = ?
piston,
radius 100mm
piston,
radius 5mm
Physics 1B03summer-Lecture
Pressure variation with depth
Pressure increases with
depth, by an amount
P2 – P1  r gh
(if r and g are uniform).
P1
h
Proof:
Consider forces on a cylinder of fluid
P2
Physics 1B03summer-Lecture
“Gauge Pressure” : pressure difference between a
fluid and the surrounding atmosphere. It is equal to
P2–P1.
Example: a tire gauge measures gauge pressure, and
reads zero when the air inside the tire is at
atmospheric pressure.
“Absolute Pressure” is the pressure compared to
vacuum. Zero absolute pressure means a vacuum.
Example: the pressure on the surface of the
earth.
Physics 1B03summer-Lecture
Example
At what depth in water is the pressure 1 atm higher
than the pressure on the surface? That is, where is
P=2atms ?
Physics 1B03summer-Lecture
Example
What is the difference in air pressure between the floor and
the ceiling?
Physics 1B03summer-Lecture
Example
What is the total mass of air directly above a 1-metre
square, from ground level all the way to outer space?
Approximately how thick is the atmosphere, assuming
(incorrectly) that the air density is uniform?
Physics 1B03summer-Lecture