Lecture 11_190627

Question 1

Hydrostatics – Pressure

Answer 1

W(weight) = F = m * g = ρ * V * g = ρ * A * h * g

P = W / A = ρ * A * h * g / A = ρ * h * g

P = ρ * h * g > h = P / (ρ * g) ….. ρ = 1 g/cm3 = 1000 kg/m3

Pressures are additive
P2 = P1 + ρ * h * g

Question 2

Pascal’s Principle

Answer 2

P1 = P2, so

F1/A1 = F2/A2 at balance

F1 = F2 * ( A1/A2)

Question 3

Hydrodynamics

Answer 3

Flow = volume (m3) / time (s) = m3 / sec
Flow = area (m2) * velocity (m/s)
Flow = A1 * v1 = A2 * v2

velocity = Flow / Area
v2 = v1 * (A1 / A2)

Question 4

The Bernoulli Equation

Answer 4

Work = ΔKE = KEfinal – KEinitial
= ½ m * vfinal^2 – ½ m * vinitial^2

Work = F1 * d1 – F2 * d2 = P1A1d1 – P2A2d2

For an incompressible fluid, A1d1 = A2d2 = V
Dividing by V yields:
P1 – P2 = ½ ρ * (v2^2 – v1^2)

Question 5

Venturi Tube Flowmeter

Answer 5

From the Bernouli equation:
P1 – P2 = ½ ρ * (v2^2 – v1^2) and v2 = v1 * (A1 / A2)

P1 – P2 = ½ ρ * v12 * ((A1/A2)2 – 1)

NOTE: the velocity determined from the pressure depends on ρ of measurement device.

Question 6

Viscosity

Answer 6

P1 – P2 = 8 * π * η * v * L / A

where (P1 – P2) is the pressure drop in length L of the tube, η is the viscosity of the fluid, v is the velocity of the fluid, L is length, and A is the area

v = (P1 – P2) * A / (8 * π * η * L)

Flow = A * v = (P1 – P2) * A2 / (8 * π * η * L)

Question 7

Poiseuille’s equation

Answer 7

assume a round tube, A = π * r2, so

Flow = (P1 – P2) * π2 * r4 / (8 * π * η * L)

canceling π gives Poiseuille’s equation:

Flow = (P1 – P2) * π * r4 / (8 * η * L)

Question 8

Electrical Circuits

Answer 8

Charge
charge on an electron, e:
e = 1.602e-19 C (Coulomb)
1 C = 6.24e+18 e

Coulomb’s Law
F = k * q1 * q2 / r2
k = 8.99e+9 N*m2/C2 (Coulomb’s constant)

F can be positive (repulsive) or negative (attractive) – opposites attract otherwise this looks just like gravitational attraction between all matter

Question 9

Electric potential energy

Answer 9

Force between 2 charges, one of them is free to move = work will be done (F * d). So there is “potential” energy that can be converted to kinetic energy – much like we saw for gravity.

U = kqq0/r
Electric potential energy has units of Joule

Electric Potential

The electric potential is normalized for charge:

V = U/q0 = K*q/r
Electric potential has units of Joule/Coulomb
1 Volt = 1 Joule / Coulomb

Question 10

Electric Current

Answer 10

Electric field → An electron placed in the field would move to the + end. Electric current is this movement of electrons.

Current is measured in charge / time
1 Amp = 1 Coulomb / second

Question 11

Conductors

Answer 11

carry electrical current efficiently – metals are generally good conductors.

Question 12

Insulators

Answer 12

resist carrying electrical current – most non-metals are insulators.

Question 13

Ohm’s law

Answer 13

Ohm’s law:

I = V / R

Where I is current (Coulombs / sec), V is voltage, and R is resistance.

Resistance is measured in Ohms (Ω) :

1 Ω = 1 Volt / Amp

Question 14

Conductance

Answer 14

Conductance (G), measured in mho or (S) siemens is the opposite of resistance:

G or S = 1 / R

mho = S = 1 / Ω = 1 Amp / Volt

Question 15

Resistors in Series

Answer 15

Rtotal = R1 + R2 + …. Rn

Question 16

Resistors in Parallel

Answer 16

Gtotal = G1 + G2 + … Gn

1/Rtotal = 1/R1 + 1/R2 + … 1/ Rn

Question 17

Electrical Power

Answer 17

Power is current times voltage.

P (W) = I (A) * V (V)
1 watt (W) = 1 amp (A) * 1 volt (V)  
or  J/sec = C/sec * J/C = J/sec

by Ohm’s law (I = V / R), the power dissipated by a resistor is:
P = I * V = V2 / R = I2 * R

In the US, most appliances use 120 V AC (alternating current) for instance, a 60 W light draws 0.5 amps at 120 volts
60W = 0.5 A * 120 V

Question 18

Electrical Energy

Answer 18

Energy (J) = power (J/s) * time (s)

electrical energy is often expressed as kilowatt-hour:
1 kWh = 1000 W * hr

Example, a 60 W light is left on for 24 hours, how many kilowatt-hours does it consume? 60 W * 24 hr = 1440 W * hr = 1.44 kWh
In DC, 1 kWh costs ~$0.09 (9 cents/kWh), how much does it cost to leave a 60W light on for 24 hours?
1.44 kWh * $0.09/kWh = $0.13 (13 cents)

Question 19

Semiconductors

Answer 19

Semiconductors have properties of both conductors and non-conductors. They are made from Group IV semi-metals, usually silicon, as well as germanium.

(Interestingly, carbon is often used to make resistors.)

Silicon has a valence of 4 and forms a cubic crystal where each silicon atom has 4 neighbors. Pure crystalline silicon is a very poor conductor of electricity. However if a small amount of Group III (e.g. boron) or Group V (e.g. arsenic or phosphorus) is added to the silicon, then it is much more conductive.

Question 20

p-type semiconductors

Answer 20

A p-type semiconductor is a Group IV semi-metal (e.g. silicon) doped with a Group III material (e.g. boron).

Boron has a valence of 3, and so wherever a B sits in the crystal, some Si is missing an electron. This leaves a positive hole in the structure.

Question 21

n-type semiconductors

Answer 21

An n-type semiconductor is a Group IV semi-metal (e.g. silicon) doped with a Group V material (e.g. arsenic).

Arsenic has a valence of 5, and so wherever a As sits in the crystal, there is an extra electron. This leaves a negative hole in the structure.

Question 22

Diodes

Answer 22

A diode is a p-type semiconductor bound to an n-type semiconductor.

A diode will conduct electricity in one direction, but not the other direction.

Question 23

Transistors

Answer 23

SLIDES 19 & 20!!!

Question 24

Spectroscopy

Answer 24

Spectroscopy involves shining light through, or reflecting light off, a material. Wavelengths of light that are absorbed by the material will not be transmitted or reflected.

*PULSE OX!

Question 25

Beer’s Law

Answer 25

Absorbance (A) for a wavelength of light depends on the absorbtivity (a) of the material, the concentration (c) and the thickness (b).
A = a * b * c

Question 26

Alpha decay

Answer 26

usually very large nuclei

Alpha particles (He ions) are big and don’t go far, so radiation is not a problem. Unless the radioactive material is in your body already – then it’s a big problem.

SEE SLIDE 24 for rxn!!!

Question 27

Beta decay

Answer 27

β- decay
n → p+ + e- + ν̅ + energy
Neutron goes to proton + kicks out an electron

Β+ decay (positron decay)
p+ → n + e+ + ν
proton goes to neutron + kicks out a positron & neutrino
Used with PET (Positron Emission Tomography) scans C-11, N-13, O-15, F-18 are used

SEE SLIDE 25 for ex!!!

Question 28

Gamma decay

Answer 28

Gamma decay does not change the configuration of the nucleus.

SEE SLIDE 26 for rxn!!!

Question 29

Decay rate & half-life

Answer 29

Half-life (t½ ) is the time it takes for half a radioactive material to decay.

Decay constant (λ) is the inverse of the half-life.
λ = ln(2) / t½

The decay of radioactive material follows
N(t) = N(0) * e–λ*t

The shorter the half-life the quicker it decays, and the greater the activity.

Most medically relevant isotopes have short half-lives (20 min – 20 days)

*t½ increase = more difficult to manage if given to pt!

Question 30

Electromagnetic spectrum

Answer 30

E = hc/λ = h * f
**Energy increases with frequency.
h = Planck’s constant (6.626E-34 J/s)

***Energy = 1/wave length

SLIDE 28!!!