Significant Figures, Kinematics, & Dynamics
Human Voice and Resonance
It is generated by elastic cords in the larynx. The tension of the cords can be changed to change the resonant frequency of the cords, produced different frequencies.
An acorn falls from a tree. Compare its kinetic energy KE, to its potential energy PE.
KE increases while PE decreases KE depends on velocity or speed. PE depends on height. Height is decreasing when falling, and speed is increasing.
Basics of the Metric System
The second = time The meter = distance/length The kilogram = distance Units must be consistent in calculations. Volume of a cube = length x width x height = m x m x m = m^3 Note: m+m+m = 3m
Metals
have a low specific heat -they get hot fast
Gamma Particles
They are a form of electromagnetic radiation Biggest
10kg cart pulled with a force of 150N up a 4m ramp. The ramp is 1m high. Calculate the efficiency.
%e = (Work(out)/Work(in))x100 W(in) = 150N(4m) = 600 W(out) = 10kg(10m/s^2)(1m) = 100 %e = (100/600)x100 %e = 0.167 x 100 %e = 16
A 200lb man stands on his right foot while carrying a 100lb bag in his left hand. The center of mass of the bag is 12in from his center of mass. Write a relationship to find the sum of the torques about his right foot. Omit the units in your answer. (Do not include equal sign.) What does x equal?
*200x + 100(12-x) = 0* 200x + 1200 - 100x = 0 100x + 1200 = 0 100x = -1200 x = -1200/100 *x = -12*
The radius of a blood vessel is reduced by cholesterol deposits to 90% of its original value, if the flow rate is to stay the same, will the pressure
*A. increase* B. decrease C. remain the same
A small bubble and a large bubble collide forming a single bubble. The pressure inside the new bubble is
*A. lower than the pressures in both the small and large bubble* B. between the pressures that were in the small and large bubble C. larger than the pressures in both the small and large bubble D. equal to the sum of the pressures in the small and large bubble
Half Life
*The time it takes half o the nuclei in a sample to decay* Ca be measured with activity the time it takes the counts to be halved Can be measured with mass the time it takes half of the mass to decay Some isotopes have very long half lives: Uranium 238 = 4.5 x 10^9 years Some have very short lives: Indium 116 = 54 min Carbon 14 = 6,000 years Carbon 14 dating is a technique that uses this fact to determine the time since a living organism died.
Mass - Energy Equivalence
*For atomic nuclei, the mass of the parts is greater than the mass of the whole* Helium 3 has a mass of 5.0066 x 10^-27 Kg One deuterium nucleus and hydrogen nucleus can be combine to form a Helium 3 nucleus Hydrogen = 1.6727 x 10^-27 Kg Deuterium = 3.3437 x 10^-27 Kg The sum is 5.0164 x 10^-27 Kg This "mass defect" becomes energy that holds the nucleus together. E = mc^2
Specific Heats in Calories
1 calorie = 4.187 Joules
The threshold of feeling electricity is at a current of 1 mA (0.001 A) If your skin has a resistance of 10,000Ω what voltage would produce that current? A. 1 V B. 10 V C. 100 V D. 1,000 V E. 10,000 V
0.001A * 10,000R = V 10 = V B. 10V
Unit Conversion Dimensional Analysis
1 inch = 2.54 cm can be written as: 1 in/2.54 cm or 2.54 cm/1 in. 1 kg = 1000 grams. That can be written as: 10^3 g/1 kg or 1 kg/10^3 g Both fractions are equal to 1. This can be used to convert units. How many grams in 0.7 kilograms? 0.7 kg x 10^3g/1kg = 700 grams How many seconds in one year?
Rules for any lens image formation
1. A ray entering the lens parallel to the axis leaves through the focal point. 2. A ray that enters the center of the lens leaves the same direction. 3. A ray that enters the lens through the focal point leaves parallel to the axis.
Resonance happens...
1. As waves hit an object. *2. When the driving frequency matches the natural resonant frequency.* 3. When the tension equals the mass of a resonator.
A UPS truck drives is complaining about back pain. He says he bounces quite a lot in his seat. What part of his back might be bothering him?
1. Between his shoulder blades. 2. The middle of his back. *3. The lower back.*
If you make a pendulum on earth, and then bring it to the moon, the time for each swing on the moon will be.
1. Greater than on Earth *2. Less than on Earth* 3. The same as on Earth
Practice Problem: When Sanjay pushes a refrigerator across a kitchen floor at a constant speed, the force of friction between the refrigerator and the floor is
1. less than Sanjay's push. 2.equal to Sanjay's push. *3.equal and opposite to Sanjay's push.* 4.more than Sanjay's push.
When Sanjay pushes a refrigerator across a kitchen floor at a *constant speed*, the force of friction between the refrigerator and the floor is
1. less than Sanjay's push. 2. equal to Sanjay's push. *3. equal and opposite to Sanjay's push.* 4. more than Sanjay's push. The answer is 3 because there is constant speed. Since there is constant speed, there is no acceleration, and when there is no acceleration, there is no net force.
The Range of the Focal Length of the Eye
1.9 to 2 cm The image distance is fixed The focal length can be changed due to muscles
Use: 1/d(sub o)+1/d(sub i)=1/f to find the image distance when a lens with a focal length of 10cm has an object 15 cm from the lens.
1/d(sub o)+1/d(sub i)=1/f 1/15 + 1/d(sub i) = 1/10 1/d(sub i) = 1/10 - 1/15 1/d(sub i) = 3/30 - 2/30 1/d(sub i) = 1/30 d(sub i) = 1/(1/30) d(sub i) = 30
There are 4 quarts in one gallon, and one quart is 0.9463 Liters. How many liters are in 30.5 gallons?
30.5 (4q/1G)(0.9463L/1q) = 115L
Humans hear the best at the frequency of
3000 Hz
1 calorie =
4.18 J
1 Cal
= 1Kcal = 4186J
A 1.6m long steel piano wire has a diameter of 0.2cm. How great is the tension in the wire if it stretches 0.25cm when tightened.
A = (pi)r^2 F/A = Y(change in L/Lsub0) omega = F/A F = omega(A) = eYA = (change in L/L)YA = (Change in L/L)Y(pi)r^2 (0.0025m/1.6m)(2x10^11 N/m^2)(3.14)(0.0010)^2 = 980N
Accommodation
A normal eye should see an object clearly no matter how far away it is. We want the "Far Point" to be at infinity. -If an eye has a far point much less than infinity, it is near sided (myopic) A normal eye should be able to see objects very close, normal eyes can see objects as close as 25cm. We want the "Near Point" to be 25 cm. -If an eye has a near point much further than 25cm, we say it is far sighted (hyperopic).
Photon
A particle of light
Correcting Myopia
A person has a far point of 1.2 meters. What power of lens will give this person normal distance sight? 1/d(sub o) + 50D = S(sub eye) 1/1.2m + 50 = S(sub eye) 0.83D + 50D = S(sub eye) 50.83D = S(sub eye) (this is the guys eye) 50D = S(sub lens) + 50.83D S(sub lens) = -0.83D
8 - SHM and Waves
A row of identical masses and springs could produce a wave.
A(sub 1)v(sub 1) =
A(sub 2)v(sub 2)
Fluid Flow and Pressure: Bernoulli Effect in the Open (not confined to tubes)
Airplane wings are shaped so air over the top moves faster than air under the bottom. This difference in speed results in a difference in pressure, producing lift.
Blood flows from the heart into the aorta, into major arteries then into capillaries. The radius of the aorta is 1.2 cm and the blood passing through has a speed of 40 cm/s. A capillary has a radius of 4x10^-6 cm and blood flows at a speed of 5x10^-4 m/s. Estimate the number of capillaries in the body.
A(sub aorta)V(sub aorta) = A(sub cap1)V(sub cap) + A(sub cap2)V(sub cap2)... A(sub aorta)V(sub aorta) = NA(sub cap)V(sub cap) V(sub 2)N(pi)r^2(sub cap) = V(sub 1)(pi)r^2(sub aorta) N = (V(sub 1)(pi)r^2(sub aorta))/V(sub 2)(pi)r^2(sub cap) N = (0.40 m/s)/(5x10^-4) * ( A = (pi)r^2
The speed of light in a certain medium is 2.2 x 10^8 m/s. What is the index of refraction of this medium? A. 1.36 B. 1.8 C. 0.733 D. 1.62 E. 1.0 F. 3.0
A. 1.36 Because... v = c/n 2.2x10^8 = 3.0x10^8/n 3.0x10^8/2.2x10^8 = n 1.36 = n
An elastic material is found to stretch a certain amount deltaL when tensile force F is applied to each end, if the material is doubled over and the same force applied, the change in length will be:
A. 2(deltaL) B. deltaL C. (deltaL)/2 *D. (deltaL)/4* F/A = change in L/L F(1/2L)/Y2A = FL/4YA = 1/4(change in L)
How deep can a diver go in fresh water without bursting an eardrum? (Say Eustachian tubes are blocked) A. 3m B. 10 m C. 20 m D. 50 m E. None of theses
A. 3m P = ρgh 3x10^4 Pa = (1000kg/m^3)(9.8m.s^2)h Solve for h
If the maximum force an eardrum can withstand is 3N and the area of the eardrum is 1.0 cm^2 calculate the maximum tolerable pressure in the inner ear. Hint: 1mm Hg = 133 Pa
A. 3mmHg B. 300mmHg C. 3x10^4mmHg D. 2.25mmHg E. 22.5mmHg *F. 225mmHg* G. None of these.
Some people with poor vision have very thick glasses. If you want the same power of lens with a thinner lens, you could use glass with A. Higher index of refraction B. Lower index of refraction C. The same index of refraction.
A. Higher index of refraction n = c/v This is because
If you bend a metal rod in half, what happens to its length and area?
A. They both stay the same. B. The length doubles, and the area halves. *C. The length halves, and the area doubles.* D. They both double.
A child swings a yo-yo in a vertical path as shown. What is the direction of the centripetal acceleration in general?
A. Up B. Down C. Left D. Right *E. None of these* The answer is E because the answer is all of them depending on where the yo-yo is in the point in the circle. -so it is none of the directions specifically
Hyperopia is the term for A. farsightedness B. nearsighted C. blindness
A. farsightedness
Newton's Third Law of Motion
Action - Reaction -For any action, there is always an equal and opposite reaction (always puts the same amount of force back) For each force, there is an equal and opposite force. Action-reaction pairs third-law force pairs.
Net Force
All of the forces acting on an object added together
Penetration Abilities of Different Types of Radiation
Alpha Particles: stopped by a sheet of paper Beta Particles: stopped by a layer of clothing or less than an inch of a substance (e.g. plastic) Gamma Rays: stopped by inches to feet of concrete or less than an inch of lead Neutrons: stopped by a few feet of concrete
What is the most ionizing radiation out of the three types?
Alpha particles radiation
Characteristics of Waves
Amplitude Frequency -Period Wavelength -Size of wave, related to resolution
What is the surface area of a 70 kg man with a height of 1.55 m? A. 1.02 m2 B. 1.07 m2 C. 1.70 m2 D. 9.8 m2
Area(m^2) = 0.202 * W^0.425 * H^0.725 Area(m^2) = 0.202 * ((70kg)^0.425) * ((1.55)^0.725) 1.70 m2
Light as a ray
As one moves farther from a point wave source, the wave fronts become more nearly flat The farther you move from the point of the wave source (source of light), they almost become parallel -plain waves
Adhesion and Cohesion
At very close range, molecules repel A little further away, they attract.
Assuming dry skin, what is electric potential across the plates of a defibrillator? A. 6 A B. 60,000 V C. 500 V D. 1 mA
B. 60,000V
Which method(s) of heat transfer can occur in empty space? (Select all that apply.) A. Conduction B. Convection C. Radiation
B. Convection C. Radiation
The heart expends energy on various function. Which of the following takes the most energy when AT REST? A. Energy to move blood through arteries and veins B. Energy to provide pressure C. Both of these require equal amount of energy.
B. Energy to provide pressure
The half life of C-14 is 5700 years. A friend just found a hominid bone in a cave that he thinks might be 23000 years old. You decide to date the bone using the radiocarbon approach and find that it contains 1/8th of its inital proportion of C-14/C-12. Was the age of the bone estimated by your friend correct? A. yes B. no C. can't tell
B. No
The best way to feel the heat from *convection* due to an open fire would be to A. Put your hand in the fire B. Put your hand over the fire C. Put your hand beside the fire
B. Put your hand over the fire
Someone who is color blind probably has probelms with: A. rods B. cones C. retina D. lens
B. cones
Ball Under Water
Ball is submerged Buoyant force more than weight Net force is up Ball breaks the surface, Buoyant force starts to decrease Net force up is decreasing Equilibrium - Weight equals buoyant force
Electric Energy Storage
Can be stored in a common device called a *capacitor*. The simplest capacitor is a pair of conducting plates separated by a small distance, but not toughing each other. When the plates are connected to a charging device, such as the batter, electrons are transferred from one plate to the other.
Find the image distance formed by a convex lens (f = 5 cm ) with an object 10 cm from the lens A. 2 cm B. 5 cm C. 10 cm D. 15 cm E. 50 cm
C. 10 cm (1/d(subi)) + (1/d(sub o)) = 1/f (1/d(subi)) + 1/10 = 1/5 (1/d(subi)) = 1/5 - 1/10 (1/d(subi)) = 2/10 - 1/10 (1/d(subi)) = 1/10 d(sub i) = 1/(1/10) d(subi) = 1 x 10 d(sub i) = 10 There is this type of symmetry for all convex lenses in air.
The electric field at point P due to a charge Q a distance R away has magnitude E. In order to double the field at P, you could A. Double the charge to 2Q and at the same time reduce the distance to R/2 B. Reduce the distance to R/2 C. Double the charge to 2Q D. Double the distance to 2R E. Reduce the distance to R/4
C. Double the distance to 2Q E = Q/R^2 to double E: E = Q/R^2 2Q/R^2 = 2(Q/R^2)
Food provides energy for human activity. This energy can be measured in A. Watts B. Volts C. Joules D. Newtons E. None of these
C. Joules
The nuclei of He are also known as A. γ (gamma) rays. B. β (beta) particles. C. α (alpha) particles. D. K-rays. E. X-rays.
C. α (alpha) particles.
Light is part of the Electro-Magnetic Spectrum
Can be modeled as a wave -x-rays -gamma rays Can be modeled as a ray -lenses -mirrors -image formation Can be modeled as a particle -modeling vision -how rods and cones perceive light
Cohesive Forces
Causes surface tension A molecule in the center of a liquid drop experiences forces in all directions from other molecules. A molecule on the surface, however, experiences a net force toward the drop. The angle can indicate the amount of surface tension. -Water droplet on wax paper creates bigger angle (it stays more in droplet form) -Water droplet on glass creates smaller angle (it spreads out more)
Acceleration
Change in speed or velocity Change in velocity/change in time 9.8m/s/s is an acceleration m/s^2 or ms^-2 Will be constant or zero - for purposes of this class Acceleration has a direction If the direction of the acceleration is the same as the velocity, then the speed will increase If the direction of the acceleration is opposite that of the velocity, then the object will slow down. It is possible to have negative acceleration and be speeding up because negative just indicates direction. When there is constant speed, acceleration is always equal to 0.
Fluid Statics and Dynamics in Humans
Circulatory System -energy and power Respiration (ventilation) Spinal Cord Eyes
What Causes Pressure
Collisions exert forces and hence pressure on the container walls. The pressure depends on the average magnitude of these
Tomograph CT or CAT
Computre Aided Tomography is not an advancement in "application of radiation" but a result of the computre
Methods of Heat Transfer
Conduction Convection Radiation
Consequences of High Exposure to Radiation: Dose (Sv) = 2 to 5
Consequence: Hemorrhaging, ulcers, LD 50
Consequences of High Exposure to Radiation: Dose (Sv) = 1 to 2
Consequence: Loss of hair, nausea
Consequences of High Exposure to Radiation: Dose (Sv) = 0.5 to 1
Consequence: Significant decrease in white blood cell count, lesions
Consequences of High Exposure to Radiation: Dose (Sv) = 0.5
Consequence: Small decrease in white blood cell count
F sub c
Contact Force It is not the normal force We don't know if the block is sliding (block on a hill - F sub c is the force acting up on the box)
Electric Field Lines
Convenient way of visualizing the electic field 1. Point in the direction of the field vector at every point 2. Start at positive charges or infinity 3. End at negative charges or infinity 4. Are more dense where the field is stronger The charge on the right is twice the magnitude of the charge on the left (and opposite in sign), so there are twice as many field lines, and they point towards the charge rather than away from it (based on picture in class)
There is an arm holding a 4kg weight. The length (moment arm) from the elbow to the weight is 40cm. What is the torque acting on the elbow?
Convert 40cm to meters = 0.4m 4kg x .4m = 1.6Nm
Measurement of Activity
Counts per minute (cpm) is the typical unit of radioactivity You might see a pico Curie (pCi) The concentration of radiation in the air is measured in pico-curies per liter If there is 4 pic-ci/liter you should test again because it is right on the border/baseline?
Quality Factor
Different types of radiation have different effects on living cells. The quality factor, Q, allows the effects that different radiations have on living cells to be compared.
A resistor is connected to a 3.0 V battery; the power dissipated in the resistor is 1.0 W. The battery is traded for a 6.0 V battery. The power dissipated by the resistor is now A. 1.0 W B. 2.0 W C. 3.0 W D. 4.0 W
D. 4.0 W
Pressure depends on what
Depth Change in P = ρg x change in h
Displacement
Distance with direction -where you are relative to an origin --ex: 5 m east of the door d = v(sub av)t v(sub av) = change in distance/change in time d = v(sub i)t + (1/2)at^2
Radiation
Does not need a medium to propagate (travels through space) Electric-magnetic waves transmit the energy Spectrum of electromagnetic radiation High frequency x small wave length Low frequency x large wave length gamma rays x-rays *visible light* *infrared* *microwaves* radio waves
What if the force is not perpendicular?
Draw the forces on the lever, if it is modeling the forearm. The force on the forearm is not vertical, but at an angle to the vertical What is the fulcrum? -(the elbow)
Cohesion
Due to atomic forces... The attraction of like molecules
Find the image distance formed by a convex lens (f = 5 cm) with an object 5 cm from the lens A. 1 cm B. -1 cm C. 10 cm D. 0 cm E. ∞
E. ∞
5 grams of Praseodymium has a half life of 30 minutes. How many grams are left after an hour and a half. A. 10 grams B. 5 grams C. 2.5 grams D. 1.25 grams E. 0.625 grams F. 0 grams.
E. 0.625 grams
You are standing 3 meters in front of a mirror. To take a picture of yourself in the mirror, you would need to set the camera focus to: A. you cannot take a picture of yourself in the mirror B. 3 m C. 0 m D. 1.5 m E. 6 m
E. 6 m This is because it is double the length that you see from so you need to double the focus.
On a cold winter day , the temperature outside is -5 degrees. Which temperature is twice as hot? A. -10 degrees B. +5 degrees C. 0 degrees D. +10 degrees E. None of these
E. None of these The temperature must be in Kelvin to be "twice as hot" Zero on the Celsius scale and zero on the Fahrenheit scale don't mean nothing. In other words, there is still energy present at 0 degrees F and 0 degrees C. -5 degrees F = -20.5 degrees C -20.5 degrees C = 252.6 K Twice 252.6K = 505.2K That becomes 449.7 degrees F
he atomic number is equal to the number of what particles in the nucleus? A. nucleons B. electrons C. positrons. D. neutrons E. protons
E. protons
Power and energy in moving blood
Each term in the parentheses represents power for a different purpose. 1/2ρv^2F is Kinetic power PF is pressure power ρgh is negligible for the heart Power = (ρgh + P + 1/2ρv^2)F
Electrical Potential => Volts
Electrical potential is similar to gravitational potential -charges will move spontaneously from high to low voltage -as they move, potential energy is converted to other forms (light, heat) -some agent (a battery, a power supply, a power station) provides energy so they can complete the circuit again. -*a volt is a joule per coulomb* -voltage is sometimes thought of as a pressure
Energy Requirements of Humans
Energy for activities depends upon the surface area of the body Area(m^2) = 0.202 * W^0.425 * H^0.725 -W is the mass Activity: Metabolic rate -Sleeping: 35 -Sitting upright: 50 -Standing: 60 -Walking 3 mph: 140 -Bicycling: 250 -Running: 600 -Shivering: 250
Electro-Mag Ionizing Radiation
Energy from the radiation changes a stable molecule into a *free radical* *UV* or higher frequency The Energy in a photon depends upon the frequency *There is also ionizing radiation from the nucleus.* -Gamma Rays
Alpha Decay
Energy is lost by the nucleus There is a change in both atomic number and mass number
Newton's Second Law of Motion
F = ma -Force = mass x acceleration -Involves a vector (direction matters) The sum of the forces is proportional to the acceleration Net force is the same as the sum of the forces
Kinetic Energy
Energy of motion. More mass, more kinetic energy. Speed is squared, double the speed, KE is FOUR times as great. Can NEVER be negative. When positive work is done on an object, its speed increases; when negative work is done, its speed decreases. If you have no mass, you have no kinetic energy. KE = (1/2)mv^2
A courier is delivering a 5.5 kg package to an office high in a tall building. What upwards force does the courier apply to the package when carrying it horizontally at a constant velocity of 2 m s−1 into the building?
F = m*a (in this case the acceleration is gravity) F = m*g F = 5.5kg * 10m/s^2 F = 55N This is because the upward force that is applied is gravity.
Rods
Extremely sensitive to light Single photon response Low spatial resolution B&W night vision
If the radius of a blood vessel is reduced by cholesterol deposits to 90% of its original value, flow will decrease. By what factor would the pressure difference along the vessel have to be increased to get the flow rate up to its original value?
F = (deltaP(pi)r^4)/(8nL) deltaP = (F8nL)/(pi)r^4 P'/P = r^4/r'^4 = 1^4/0.9^4 = 1.5 P' is the original number P is new number
Centripetal Force
F = (m)(v^2/r) When moving in a perfect circle, the net force is the centripetal force Always toward the center of the circle
Hooks Law
F = -kx Force on block due to spring x = position of block k = spring constant or stiffness constant (N/m)
A courier is delivering a 5.5 kg package to an office high in a tall building. How much work does the courier do to the package when carrying it horizontally at a constant velocity of 2 m s−1 into the building?
F = m*a F = 5.5kg x 0m/s^2 F = 0N W = F*d W = 0*d W = 0J
Work (Done by a Constant Force)
Force through a distance W = Fd -When the force is parallel to the displacement. W = (Fcos(theta))d = Fdcos(theta) SI unit: newton-meter (Nm) = Joule (J) Work is not a form of energy in the same sense as kinetic energy or potential energy. "Work" instead describes the amount of energy being changed from one form into another by a force. If the force is acting in a direction other than the motion of the object, there is no work being done. -This is why the angles are important The work done may be postive, zero, or negative, depending on the angle between the force and the displacement. -W = positive if theta < 90degrees -W = 0 if theta = 90degrees -W = negative if theta > 90degrees
P =
Force/A
Damped Harmonic Motion
Friction in the spring, or the medium will cause the vibration to quickly stop. This oscillator is under damped - it doesn't stop right away.
Rank the following types of electromagnetic radiation in order of increasing wavelength (short to long). 1st choice visible 2nd choice ultraviolet 3rd choice microwave 4th choice gamma 5th choice radio
Gamma Micro UV Visible Radio
The Thin-Lens Equation
Gives us the thin-lens approximation, as well as the magnification: (1/d(subi)) + (1/d(sub o)) = 1/f d(sub i) is the image distance d(sub o) is the distance of the object from the lens h(sub i)/h(sub o) = d(sub i)/d(sub o) The further away the image is from the lens, the bigger that it appears to be.
Gravity and Circulatory System
Gravity affects pressure but not flow rate. -does not affect flow rate of a closed system Gravity does not affect flow rate in any closed system -similar to how atmospheric pressure has no effect on flow in an IV Gravity pulls down on both sides of the "tube."
How much heat must be added to a 8kg block of ice at -8 degrees C to change it to water at 14 C in kcal.
H(sub f) ice = 80 cal/gr or Kcal/kg C water = 1 cal/gr C or Kcal/kg C C ice = 0.5 cal/gr C or Kcal/kg C delta Q = mc(delta T) delta Q = mh Cold ice to ice at 0: -8 to 0 degrees delta Q = mc(delta T) = 8kg(0.5)8C = 32kcal Ice to water: melt delta Q = mL(sub f) = 8kg(80) = 640kcal Water to warmer water: 0 to 14 degrees delta Q = mc(delta T) = 8kg(1)14C = 112kcal 32 + 640 + 112 = 784kcal
Energy and Power Supplied by the Heart
Heart does work in lifting blood as well as increasing the speed of the blood. So, in mechanics we "do work" on objects or increased the speed of an object. Now we will look at work per unit volume Energy/Volume or E/V PE = mgh +PV PE/V = (mgh/V) + P = ρgh + P KE = 1/2mv^2 KE/V = (1/2mv^2)/V = 1/2ρv^2 E/V = PE/V + KE/V = ρgh + P + 1/2ρv^2
A block with a mass of 1.0kg slides down a ramp at a *constant speed.* What is the net force on the block?
Hint: F=ma *A. 0.0N* B. 1.0N C. 10.N D. Need to know more information to answer. The answer is A because there is constant speed/velocity. This means that the acceleration is 0. F = 1.0kg x 0m/s^2 F = 0N
Example of Newton's Second Law of Motion
His mass (120 kg) is the same on the earth as well as the moon , his weigh on the moon (200 N) is of that on earth (1200 N)
Dosimitry
How much is too much? Risk assessment Measurement of radiation
Elasticity: Stress and Strain
How objects change when a force is applied.
Free Fall and Acceleration Due to Gravity
In the absence of air friciton, all things fall with an acceleration of 9.8m/s^-1 -we are going to round it up to 10m/s^-1 This is INDEPENDENT of the horizontal motion.
Intensity
I is the physical measure of intensity Perception is not linear The Decibel scale is set up to describe the perceived loudness of a sound. I(sub 0) is the threshold of human hearing = 1x10^-12 W/m^2 I = (energy/time)/area = (E/t)/A L(sub1) = 10log(sub10)(I/Isub0)
The Electric Field
If we know the electric field, we can calculate the force on any charge: The symbol q in the equation is the quantity of charge on the test charge (not the source charge). Recall that the electric field strength is defined in terms of how it is measured or tested; thus, the test charge finds its way into the equation. Electric field is the force per quantity of charge on the test charge. The direction of the force depends on the sign of the charge - in the direction of the field for a positive charge,
Medical Uses of Radiation
Imaging: -traditional x-ray CT or CAT scan or MRI Killing Cells: -alpha -beta -gamma -x-rays -radio waves (non ionizing)
Newton's First Law of Motion
Inertia -An object in motion will stay in motion and and an object at rest will stay at rest unless acted upon by an outside force.
Surface Tension
Intermolecular bonding on liquid surfaces causes the liquid to minimize its surface area and resist deformation of its surface. Y = F/L surface tension = force / length Depends on how much content there is between the surface and liquid
Pressure Scale
Involves: -Gauge pressure -Absolute pressure absolute pressure = gauge pressure + absolute atmospheric pressure
Simple Harmonic Motion
Involves: -displacement -amplitude -cycle -period -frequency
Resonancy
Involves: -natural frequency of vibration -driving frequency When it is occurring, there is a situation in which interference happens. -there will be a standing wave
Binding Energy and Nuclear orces
Iron is the most stable isotope
Current
Is a flow of charge -it is not really a flow of electrons, but we can think of it that way Current is Coulombs per second I = q/t (q can be heat or charge - typically, Q = heat and q = charge) 1 Amp = 1C/s in all circuits, the number of charges is conserved, so the current into a junction = the current out.
Heat and Mechanical Work
James Joule used a device similar to the one shown in the picture (on the slides) to measure the mechanical equivalent of heat Mechanical work is equivalent to heat
Projectile Motion
Know that the horizontal motion is separate from the vertical motion.
Example of Intensity: A sound has a loudness of 30db. What is the intensity of the sound?
L(sub1) = 10log(sub10)(I/Isub0) 30 = 10log(sub10)(I/10^-12) 3 = log(sub10)(I/10^-12) 10^3 = I/10^-12 10^3(10^-12) = I I = 10^-9 Check: Lsub1 = 10log(sub10)(I/I(sub0)) Lsub1 = 10log(sub10)(10^-9/10^-12)
This person is walking "boldly" with big steps. The length of her leg is 90 cm. What is the time for one complete step
Make sure to convert Ncm to Nm T = 2(pi) x squrt(L/g) T = 2(pi) x squrt(9m/10m/s^2) T = 6.28 x squrt(0.9) T = 6.28 x 0.3 T = 1.8
Ray Tracing for Lenses
Lenses focus light and form images. Consider only the symmetric ones, the double concave and the double convex.
Refraction
Light changes direction due to a change in speed caused by the medium. A ray of light is incident as shown from air (n=1) onto a transparent slab whose index of refraction is n=1.3. The slab has a thickness of 0.01m. Show the direction of the emerging ray as it leaves the glass.
Forming Images with a Plane Mirror
Light reflected from the flower and vase hits the mirror. Obeying the law of reflection, it enters the eye. The eye interprets the ray as having had a straight-line path, and sees the image behind the mirror
Characteristics of Sound
Loudness Pitch Audible Range Ultrasound Infrasound
ρ =
M/V
Converging Lenses
Makes the light come together. The medium is convex -the edges are thinner than the middle If we think of a convex lens as consisting of prisms, we can see how light going through it converges at a focal point (assuming the lens is properly shaped). The convex lens forms different image types depending on where the object is located with respect to the focal point.
Diverging Lenses
Makes the light go away from each other. The medium is concave -the edges are thicker than the middle A concave lens can also be modeled by prisms, but they spread apart from the focal point.
Tire Pressure
Measured in gauge pressure 42 PSI is gauge (pounds per square inch) The absolute pressure would be (42 + 14.7)
(Y) Young's Modulus
Modulus means a factor or ratio Tells the "stiffness" of a substance Ycompression = compressive stress/compressive strain OR =tensile stress/tensile strain =(F/A)/(change in L/ Lsub0) omega = Ye
Efficiency of Machines
Most machines lose energy. -friction -thermal heat -etc An ideal achine would lose no energy and have an efficiency of 100% %e = Work(out)/Work(in) -Work out is the change in gravitational potential energy
Medical Application to Resonance
Motion of the spine
What type of lenses correct myopia (nearsightedness)
Negative lenses
Equillibrium
Net force = 0
Gamma Decay
No change in mass, but the nucleus loses energy
Centrifical Force
Not a true force
Kinetic Theory
Not all molecules in a gas will have the same speed; -their speeds are represented by this distribution, and depend on the temperature and mass of the molecules *Temperature is related to the average kinetic energy of the molecules.*
Half-Life and Rate of Decay
Nucleaer decay is a random process; the decay of any nucleus is not influenced by the decay of any other.
Temperature and the Zeroth Law of Thermodynamics
Objects are in thermal contact if heat can flow between them. When the transfer of heat between objects in thermal contact ceases, they are in thermal equilibrium. The most fundamental law out of the 3 laws of thermodynamics
Bernoulli's Equation is: P+(1/2ρv^2)+ρgh Write this express IF there is NO FLOW, that is if v = 0 Write this express IF there is flow, but the height is constant...
P + ρgh (1/2)ρ(v(sub 2)^2 - v(sub 1)^2)
Diagram of 3 forces acting on the elbow when lifting a weight
One force acting downwards (the weight) One force diagonally pulling up (the bicep contracting and lifting the weight) One force pulling up (the tricep pulling on the arm) Counter clock wise is negative Does the fulcrum exert a force? -yes Why does it not exert a torque? -the lever arm has a length of zero The torque of the weight plus the torque of the tendon is equal to 0 making it in equilibrium.
Beta Decay
One neutron becomes a proton and an electron Note the change in atomic number, but not in mass number The electron is ejected This leads us to believe that a neutron is composed of an electron and a proton
Free Radical Theory
Organisms age because cells accumulate free radical damage with the passage of time. For most biological structures free radical damage is closely associated with oxidation damage. Way too much ionizing radiation will result in quick death. A medium amount would lead to cancer. Normal amounts, the body can deal with.
Pressure
P = F/A Pressure is force per unit area. 1N/m^2 = 1Pa Normal atmospheric pressure is around 100kPa
Electrical Power
P = VI = V(q/t) = (W/q)(q/t) = W/t P = VI = (IR)I = I^2(R) P = VI = V(V/R) = V^2/R
Bernoulli Equation
P(sub
This guy has a mass of 80Kg. His C.G. rises 0.25 meters during one pull up. What is the change in his Gravitational potential energy when he goes from the bottom to the top of the pull up? Use 10 m/s/s for g
PE = mgh PE = 80x10x0.25 PE = 200J
This guy has a mass of 80kg. Assuming his muscles are 50% efficient, how many Joules will he use in one pull up if his C.H. rises 0.25m during the pull up?
PE = mgh PE = 80x10x0.25 PE = 200J 200J x 0.5 = 100J or %e = Wo/Wi 0.5 = 200J/Wi 200J/0.5 = Wi 400J = Wi
Matter and phase change
Phase change requires a change in potential energy
What type of lenses correct hyperopia (farsightedness)
Positive lenses
For the left ventricle, the speed of the blood is 30 cm/sec, the flow rate is 83 cm^3/sec, the density of blood is 1.05 g/ m^3 and the pressure is 120 mm Hg = 1.60x10^4 N/m^2. Find the pressure power in the left ventricle.
Pow = (ρgh +P +1/2ρv^2)F Pow = (P)F F = 83cm^3/s(1m^3/1x10^6 cm^3) = 83x10^-6 P = 1.60x10^4 Pow = (83x10^-6)(1.60x10^4) Most work is done by left ventricle -kinetic
Power
Power is a measure of the rate at which work is done: P = W/t SI unit: J/s = watt (W) 1 horse power = 1hp = 746W If an object is moving at a constant speed in the face of friction, gravity, air resistance, and so forth, the power exerted by the driving force can be written: P = Fd/t = F(d/t) = Fv
Pressure Due to a Fluid
Pressure is due to the weight of fluid above you. The weight of the volume of fluid above area A is the force of pressure Ph = Psurface + ρgh P = force/area = mg/A = (ρhA)g/A P = ρgh
Radiation Type: Gamma Rays
Quality Factor (Q): 1
Radiation Type: X-Rays
Quality Factor (Q): 1
Radiation Type: Beta Particles
Quality Factor (Q): 2 to 3
Radiation Type: Alpha Particles
Quality Factor (Q): 20
Radiation Type: Neutrons
Quality Factor (Q): somewhere between alpha and beta
The Refraction of Light
Refraction can make objects immersed in water appear broken, and can create mirages Light moves at different speeds through different media. When it travels from one medium into another, the change in speed causes the ray to "bend." From air to water, the refraction bends toward the normal -faster to slower From water to air, the refraction bends away from the normal -slower to faster
Angle of Refraction
Related to different speeds: (sin(theta sub 1))/(v sub 1) = (sin (theta sub 2))/(v sub 2) The speed of light in a medium is given by the index of refraction of that medium: Index of Refraction: n v = c/n n = c/v c = 3.0x10^8 m/s
Cones
Relatively insensitive to light 100 photos for response comparable with rods High spatial resolution 3 types of cones - color, frequency, range Color daylight vision -primary colors are red, blue, and green
For the Optics of the Eye
S = strength (or power) of lens S = 1/, when f is in meters S has units of diopters (D) Normal eye has a strength of 50.0 D Distance from lens to retina in human eye is 2.0cm S = 1/f = 1/.02m = 50.0 D
Corrective Lenses
S(sub total) = S(sub corrective lenses) + S(sub eye) 1/d(sub o) + 1/d(sub i) = S(sub eye) -> 1/d(sub o) + 50.0 D = S(sub eye)
Archimedes Principle
Says the weight of the displaced fluid is equal to the buoyant force.
Circuit Elements Can be in Parallel or Series
Series Circuit: if one breaks or turns off, then they all don't work (because there is only one path) -no branches -one path for current -energy per charge loss as charges move through circuit -I(sub 1) = I(sub 2) = I(sub 3) = I(sub b) -V(sub b) = V(sub 1) + V(sub 2) + V(sub 3) Parallel Circuit: -branches -more than one path -current splits and then combines -V(sub 1) = V(sub 2) = V(sub b) => voltage going through equals the voltage through the battery -I(sub b) = I(sub 1) + I(sub 2)
Significant Digits
Significant digits are ones that have precision, not magnitude. -35m has 2 sig figs, 204 sec has 3 sig figs. -Ones that have the most precision are the ones with most sig figs. 2000 meters and 2 x 10^2 meters have the same number of sig digits, (one) and therefore the same precision. -2000. meters is 2.000 x 10^3 meters in scientific notation Ex: Which one is the most precise? A. 2.0 x 10^2 (has 2 sig fig) B. 2.00 x 10^0 (has 3 sig fig) C. 2000 (has 1 sig fig) D. 2 x 10^2 (has 1 sig fig) Answer is B since it has 3 sig fig.
A light bulb has 0.8 Amps of current flowing through it. What is the resistance of the bulb? A. 96 Ω B. 150 Ω C. 0.007 Ω D. 120 Ω E. None of the above
Since the standard voltage is 120 120V = (0.8A)(R) 120V/0.8A = R 150Ω = R
Deceleration
Slowing down (opposite of acceleration) It is possible to have positive deceleration and be slowing down because positive just indicates direction.
Surfactant
Some kind of liquid that reduces the liquid's surface tension. A shortened form of surface - active agent. The molecules of this tend to concentrate near the surface. Soap in water acts as this.
Types of Waves: Longitudinal
Sound waves consists of compression and rarefactions. pushes the molecules left and right as the wave travels from left to right. -median vibrates in the same direction as the wave travels.
Velocity
Speed with direction change in displacement/change in time north at 10m/s is a velocity 17m/s at 35 degrees v(sub av) = (1/2)(vi +vf) change in velocity = at a = change in velocity/change in time (for these equations acceleration must be constant)?
Standing Waves; Resonance
Standing waves occur when both ends of a string are fixed. Nodes, where the amplitude is always zero. - in between the crest and trough Antinodes, where the amplitude varies from zero to the maximum value. - crest
Pascal's Principle
States that pressure applied to an enclosed fluid is transmitted undiminished to every part of the fluid as well as the walls of the container. P(sub x) = P(sub y) or F(sub x)/A(sub x) = F(sub y)/A(sub y)
Gravitational Potential Energy
Stored energy. W=Fd=Fh=mgh PEgravitational = mgh PEgravitational = wh Energy stored in the Earth's gravitational field. Conservation of energy. -if you pick something up that stored potential energy is in that object. Then, if you drop it, that will change to kinetic energy.
The Period and Sinusoidal Nature of SHM
T = 2(pi) x squrt(m/k) f = 1/T = 1/(2(pi)) x squrt (k/m)
Matter and temperature
Temperature depends on the average of speed of the molecules
Kinetic Energy and Mechanical Energy
The NET work done = the change in kinetic energy. (work energy theorem) change in work = change in kinetic energy Friction takes away from the NET work.
Resistance
The ability of an object to resist the flow of current. Depends upon: -diameter of the conductor -length of a conductor -material of the conductor ---metals conduct electricity very well Temperature - lower the temp, less resistance
Adhesion
The attraction of different molecules
Dose Equivalent
The biological effect of radiation depends on: -the type of radiation -the type of body tissue or body organ that absorbs the radiation -the total amount of energy abosrbed -this is where the quality factor (Q) comes in This is a measure of the biological effect of radiation and it takes account of the type and energy of the radiation as well as how the radiation is distributed. -rem -Sv -measured in Sv. rem is the older unit An alpha is 20 times more dangerous than a gamma, if they have the same energy.
Heat
The energy transferred between objects because of a temperature difference -internal energy Different from temperature Measured in Joules or Calories
The parts of the eye
The eye is an essential system with a lens and screen. The lens forms a real image on the retina, which acts like a screen. Refraction occurs at all interfaces...
Fluid Flow and Pressure: Bernoulli Effect
The faster a fluid flows, the lower the pressure.
Electric Circuits
The flow of electricity Electric potential is volts Electric current is amperes or amps Electric resistance is ohms *Ohm's Law* -generalization that helps describe how electricity flows V = IR V = electric potential (the standard volts is 120 so if it is not told in a problem, use 120) I = current (amps) R = resistance (ohms)
Near Point of the Eye
The focal distance is about 1.85cm when the object distance is set at a near point The near point is about 25cm.
Far Point of the Eye
The focal distance is about 2cm when the object distance is set at infinity The far point is set at infinity
Coulomb's Law
The forces on the two charges are action-reaction forces F =
Easy way to how much decays... (don't need formula from text)
The half life of indium-116 is 90 minutes. If we start with 2 grams of In-116, how much is left after one day? 1/2^n 1 day is 24 hours 24/1.5 = 16 half lives 2(1/2 * 1/2 * 1/2 * Or 2(1/2^16) = 3.0 x 10^-5 grams
Specfic Heats
The heat capacity of an object is the amount of heat added to it divided by its rise in temperature: Definition of Specific Heat, c c = Q/(m)(delta T) SI unit: J/(kg * K) = J/kg * C degrees) Q is positive if delta T is positive; that is, if heat is added to a system Q is negative if delta T is negative; that is if heat is removed from a system
Intensity of Sound: Decibels
The intensity of a wave is the *energy* transported per unit time across a unit area (amplitude) The human ear can detect sounds with an intensity as low as 10^-12 W/m^2 and as high as 1 W/m^2 Perceived loudness, however, is not proportional to the intensity. -our ears are not linear so we measure in decibals
Isotope
The isotope number refers to the number of neutrons and protons The nuclei with the same atomic number and mass number are the same isotope Nuclei with the same atomic number, but different mass number are different isotopes. For example: these element are the same element but different isotopes.
The Reflection of Light
The law of reflection states that the angle of incidence equals the angle of reflection Law of Reflection theta (sub r) = theta (sub i) theta sub r is the reflective wave theta sub i is the incident wave Reflection from a smooth surface is called specular reflection; if the surface is rough, it is diffuse reflection
Constructive Interference
The net result of the waves is equal to the sum of the waves -results in a bigger wave
Some Basic Notation
The nucleus is at the center of the atom. It contains protons and neutrons -the protons are positively charged -the neutrons are neutral -both are 2000 times heavier than the electron When you write down a symbol for nucleus, -the super script is the atomic mass number, and it is the number of protons and neutrons (the addition of protons and neutrons) -the sub script is the atomic number and it is the number of protons -For example, this has 1 proton and 1 neutron.
Significant Figures
The number of significant figures is the number of reliably known digits in a measurement. It is usually possible to tell the number of significant figures by the way the number is written: 23.21 cm has 4 significant figures 0.062 cm has 2 significant figures (the initial zeroes don't count) 80 km has 1 significant figure. If you mean 2 sig fig, write 80. km. If it has 3, write 80.0 km. When multiplyig or dividing numbers, the result has as many sig figs as the number used in the calculation with the fewest sig figs. Ex: 11.3 cm x 6.8 cm = 77cm^2 When adding or subtracting, the answer is no more accurate than the least.......
Temperature Scales
The pressure in a gas is proportional to its temperature. The proportionality constant is different for different gases, but they all reach zero pressure at the same temperature, which we call absolute zero. The Kelvin scale is similar to the Celsius scale, except that the Kelvin scale has its zero at absolute zero. Conversion between a Celsius temperature and a Kelvin temperature: T = T(sub C) + 273.15
Forced Vibrations; Resonance
The sharpness of the resonant peak depends on the damping. -If the damping is small (A), it can be quite sharp -If the damping is larger (B), it is less sharp Like damping, resonance can be wanted or unwanted. -musical instruments and TV/radio receivers depend on it.
Position vs Time Graph
The slope of the position versus time graph is the velocity. The change in x = 20m - 15m = 5.0m The change in t = 6.0s - 4.0s = 2.0s The speed is change in x/t = 5.0m/2.0s = 2.5m/s This speed is positive, the object is moving away from the origin. (based on in class example)
Wave Speed in Solids
The speed of sound is different in different materials; in general, it is slowest in gases, faster in liquids, and fastest in solids. The speed depends somewhat on temperature, especially for gases. The speed of sound increases with increasing stiffness of the medium, and decreases with increasing density. This equation agrees well with the measured speed of sound in water (1482m/s at 20C)
Viscosity
The thickness of a substance -The thicker, the higher the viscosity -The less thick, the lower the viscosity The SI unit is (Pascal Second) The cs unit is the Posie cP is centiposie Water at 20 degrees C has a viscosity of 1.0020 cP
Angular Acceleration
The velocity of an object traveling in a circle at constant speed is always tangential to the circle. As the object travels around the circle the change in velocity will point towards the center (provided this is measured over a small time). This implies that the object is accelerating toward the center of the circle. Linear speed = v = change in x/change in t Angular speed = ω = change in angle/change in t angular acceleration = a = change in ω/change in t
A Standing Wave
The wave is going back and forth in the string. -the blue wave is traveling to the right, the red wave to the left. The crests and troughs line up -there is motion going to the left and it is bouncing back, but the timing is making it so that everything lines up.
Units for Measuring Radiation
There are different types of units to measure radiation Units that measure the activity of the source (cpm, Bq-, Ci - Curie) (counts per minute) Units that measure the absorbed energy due to radiation (rad) *Units that measure the biological impact of radiation (rem) or Sieverts (Sv)*
Pressure Explains Floating
There is more pressure at the bottom of an object than the top. -This gives you a net force This is due to the fact that the bottom is deeper than the top. This difference in pressure results in a force called the buoyant force Archimedes Principle
Beta Particles
They are electrons Medium size (between alpha and gamma particles)
Alpha Particles
They are helium nuclei 2p's and 2n's Smallest
Critical Damping
This is the fastest way to get to equilibrium.
Convection
Transfer of heat in a liquid or gas Warm air rising Hot air balloon Ocean breeze Only applies to fluids (sorta) Warm air is less dense, buoyancy is greater, so region of warm air rises
Conduction
Through direct contact
If a hair dryer draw 8 amps, and is connected to the 120 volt outlet, what is its resistance?
V = IR 120V = 8A*R 120V/8A = R 15 = R
A constant potential difference V is applied across two resistors connected in parallel as shown. The current through the 2-ohm resistor is 2 A. What is the current through the 4-ohm resistor, in amperes?
V = IR V = 2 ohm (2 amp) V = 4 Since V(sub b) = V(sub 1) = V(sub 2) 4 volt = 4 ohm (I) 4/4 = 1 amp
Flow =
V/t
Flow Rate
Variable to increase -viscosity (decreases flow rate) -length of tube (L) (decreases flow rate) -radius of tube (r) (increases flow rate) -pressure between input and output side (P(sub 1) - P(sub 2)) (decreases flow rate) R = (8(viscosity)L)/((pi)r^4) Flow Rate = (P(sub 1) - P(sub 2))/R Flow Rate = (P(sub 1) - P(sub 2)(pi)r^4)/(8(viscosity)L) Flow Rate = (Change in P(pi)r^4)/(8(viscosity)L)
A 1kg (about 5lb bag of sugar) can is lifted 3 meters. If it takes her one half a second to lift the can, how much power does she use?
W = Fd = mgh 1kg(10m/s^2)3m = 30J P = W/t 30J/0.5s = 60W Do this all the time, and you can power a light bulb.
Types of Waves: Transverse
Vibration is perpendicular to wave motion Light, water, ocean waves are of this type
Weight and Mass
W = mg This downward force is due to the gravitational attraction between the Earth and the object and is often called the object's weight Weight is not the same as mass. -Weight is a force -Mass is the amount of molecules that an object has
Relationship between Electric Potential and Electric Field
Work is charge multiplied by potential W = -q(Vb - Va) = -qVba Work is also force multiplied by distance W = Fd = qEd V = W/q
Bone Fracture
We will use the concept of work and energy o solve this problem Find the energy necessary to compress the bone Then, determine the height you must have for this energy. Breaking stress for bone = 1X10^4 N/cm^2 Average area = 6cm^2 F = 60,000N because: 6(1x10^4N/cm^2) = 60,000N Say bone is compressed 3mm = 0.003m W = fd = 60,000(.003) = 180J Find the height that gives you this energy: Assume that the person has a mass of 70kg (that is 154lbs) Start with 180 joules or energy 180j = mgh (potential energy) 180J = 70kg(10m/s^2)h h = 0.25m = 25cm This is a bit low realistically, it is about a half a meter
How high do you need to fall to break your leg?
Well, depends on how you fall and your mass Assume you land feet down, with all the force acting along the length of the bone (you lock your knees) When climbing stairs, to the top of a building, you do work to While bones can break in many ways, let us consider a force along the length of the bone. 1 dyn - 1x10^-5 Newtons -Use "compression" value Rupture strength: dyn/cm^2
Destructive Interference
When a wave and a trough combine, they cancel each other out -results in no wave
Specific Gravity
When floating at the surface: fraction of object submerged = ratio of density of object to density of fluid Example: Cork has a density of 0.24 g/cm^3 What fraction is submerged if the cork is floating on the surface of the water? (0.24 g/cm^3)/1.0 g/cm^3 0.24 or about one quarter is submerged by volume
Speed
change in position/change in time 10m/s is a speed (or ms^-1) When there is constant speed, acceleration is always equal to 0.
Describe the motion of the crate: This person pulls a crate 2.00 meters with a force of 120. N at an angle of 30.0 degrees to the direction of motion. The crate has a mass of 25.0 kg. How much work does the peron do on the crate?
You can't - you need more information. Ok, the force of friction is equal to 75.0N. Then the NET force on the crate is 120N*cos(30) - 75.0N = 104N - 75.0N =29.0N a = F/m a = 29N/25kg a = 1.2m/s^2
Stress-Strain Curve
Youn'gs modulus is the slope of the stress-strain curve. The material in the top graph is brittle (concrete). The material in the middle graph is slightly ductile (stiff rubber band or a spring). The material in the bottom graph is very ductile.
Centripetal Acceleration
a = (v^2)/r
Cycle
a full to-and-fro motion -over and back (not just over to one point)
Stress
a measure of the force per unit area applied to an object, and the size of the internal forces acting within the object as a reaction to the externally applied forces. omega = F/A N/m^2 = Pascal (Pa)
Overdamping
the system is slowed so much that it takes a long time to get to equilibrium. -too much friction, too much resistance so it slowly comes back to equilibrium.
Pascal (Pa)
a unit of stress and also pressure Blase Pascal It is force per unit area 1 Pa = 1Newton/Meter^2 We will see more of this in the section on fluids.
How much power does the heart generate?
about 2 Watts (W)
Audible Range
about 20Hz to 20,000Hz; upper limit decreases with age
Ultrasound
above 20,000 Hz; see ultrasonic camera focusing below
Energy in the Simple Harmonic Oscillator
at the limits of its motion, the energy is all potential. at the equilibrium point, the energy is all kinetic
Frequency and Period
f = number of waves or vibrations/time f = cycles/second (c.p.s. or Hertz (Hz)) = sec^-1 T = Time/number of vibrations (units are seconds) A period is represented by T T = 1/f f = 1/T
Infrasound
below 20Hz
Gamma radiation has a frequency of 1019 Hz. Considering this is a form of electromagnetic radiation, calculate the wavelength of this radiation. Use c = 3.0x108 m/s. c = fλ
c = fλ 3x10^8 = 10^19 x λ (3x10^8)/(10^19) = λ 3x10^-11 = λ
Period and frequency of a fly's wing-beats If the fly's wings flap, say, 200 times in one second, then the frequency of their motion is
f = 200 beats per 1 second = 200s^-1 = 200 Hz The period is 200th of a second T = 1/f = 1/200Hz = 0.005s
The elbow in physics
can represent forearm as a lever
Pressure in Bubbles
change in P = P(sub int) - P(sub ext) = 4Y/r Pressure is inverse to radius F = 2pi(r)y + 2pi(r)y = 4pi(r)y F = PA = change in P(pi)r^2
Concave Mirror
curves inward virtual image is larger and farther away than the object
Convex Mirror
curves outward virtual image is smaller and closer to the mirror than the object
Water
has a high specific heat -gets hot slow
A block of aluminum with a mass of 50 grams is initially at room temperature (20 degrees C) is placed in boiling water. How much heat energy, flows from the water into the block, after the block arrives at thermal equilibrium
delta Q = (m)(c)(delta T) = 50gr(0.217cal/g*degrees C)(100 degrees C - 20 degrees C) 886 calories = 0.68 kcal = 868 cal(4.187J/cal) 3634 J Now use Joules delta Q = (m)(c)(delta T) = 0.05kg(900Joul/kg*degrees C)(100 degrees C - 20 degrees C) = 3600J
Heat Capacity
depends on the object's mass. quantity which is a property only of the material of the specific heat Definition of Heat Capacity, C C = Q/delta T SI unit: J/K = J/Cdegrees Q = (m)(c)(delta T) -tells us how much heat we have to add to get the temperature to go up
Electricity in Cells
electrical "current" along a nerve cell
A swing goes back and forth in 2.0 seconds. What is its frequency?
f = 1/2.0s = 0.5Hz
Muscles can only pull
force depends upon cross section 7 x 10^7 N/m^2 102 lb/in^2 Bicep raises arm Tricep lowers arm -both act upwards since they only pull up
Shadow
formed by high frequency electromagnetic waves (X-ray)
Gauge Pressure
has the reference point at atmospheric pressure.
Wave Equation
gives speed of the wave
Amplitude
gives the height of the wave
Latent Heat of Fusion or Vaporization
h Q = mh SI unit J/kg or cal/gram h, is the heat that must be added to or removed from one kilogram of a substance to convert it from one phase to another. During the conversion process, the temperature of the system remains constant.
Driving Frequency
if there is a "push" the frequency of the push has to match the natural frequency of the oscillator the timing of the push on the swing has to match the frequency of the swinger
Heat is the flow of
internal energy from high temperature to low temperature
Angular Displacement
is an angle, usually theta measured in radians the arc length (s) equals the radius (r) times theta (also known as the angle) s = r(theta) theta is like x, for linear distance of displacement The relationship between the subtended angle and arc length
Absolute Pressure
is the pressure measured on a scale that has zero at a perfect vacuum.
Types of power generated by the heart
kinetic pressure
Geometrical Optics
light as a ray explains how mirrors, lenses, and telescopes work
Pressure is greater below the heart, and less above the heart
low pressure in the head can cause fainting. Larger pressure in the legs can cause edema - fluid flow from capillaries to interstitial spaces of the body. P(sub head) = P(sub heart) - ρgh(sub head) P(sub legs) = P(sub heart) + ρgh(sub legs)
Finding the Density of a Person: The mass of a person in air is 80kg and his apparent mass when submerged in water to be 2.0kg. Calculate the volume and density of the person.
m(sub fl) = 80kg - 2kg = 78kg (fluid displaced) ρ(sub fl) = m(sub fl)/V(sub fl) V(sub fl) = m(sub fl)/ρ(sub fl) = 78kg/(1x10^3 kg/m^3) V(sub fl) = V(sub p) = 7.8x10^-2 ρ(sub p) = m(sub p)/V(sub p) = 80kg/7.8x10^-2m^3 = 1.03x10^3 kg/m^3 = 1.03 g/cm^3
Displacement
measured from the equilibrium point
Strain
measures the change of shape of an object subject to a stress. -apply a stress to something and it gives it a strain Tensile: change in L is positive Compressive: change in L is negative Change in L/ L (sub 0)
Natural Frequency of Vibration
objects have a "natural" frequency This frequency depends upon the size, elasticity, and constraints on the system if the object is "tapped" it might start to swing at its natural frequency
Electrical Power for Electricity
power is still the rate at which work is done power is volts x amps watt = volt x amp
Electric Power From Mechanics
power is the rate at which work is done power = work/time watt = joule/second
Pitch
related to frequency
Loudness
related to intensity (amplitude) of the sound wave
Law of Reflection
shape of mirror forms a different virtual image involves: -convex mirrors -concave mirrors
The nucleus of an atom is composed of protons which are positively charged
some nuclei are too large to be stable -these will tend to emit particles to become more stable Invovles -alpha particles, -beta particles, -gamma particles
Wavelength
the distance from one point on a wave to the other that is at the same height
Amplitude
the maximum displacement
Frequency
the number of cycles completed per second
Focal Point
the point in space where parallel light rays meet after passing through the lens or bouncing off the mirror. A "perfect" lens or mirror would send all light rays through one focal point, which would result in the clearest image.
Size of the wave correlates with...
the size of the thing that makes the wave
Period
the time required to complete one cycle
Underdamping
there are a few small oscillations before the oscillator comes to rest.
Tube open at both ends
this is a standing wave traveling through the air in a tube there is an anti-node at both ends, and a node in the middle -air column with both ends open
Resistivity of various tissue
used in determination of percentage of body fat the resistance (actually impedance) depends upon frequency
The note "A" has a frequency of 440. Hz. If the wavelength is 78 cm, what is the speed of sound?
v = fl v = 440Hz x .78m v = 343.2 m/s
Speed for Waves
v = fl v = frequency x wavelength c = fl for electro-magnetic (light) waves Speed is independent of frequency and wave length Depends upon "stiffness" of the medium Sound travels faster in steel than air units = m/s
Current Flow - Bioelectricity
voltage applied across a metal, a current flows -electrons move under the influence of an electric field voltage is applied across a solution containing positive and negative ions, current flows -both ions move under the influence of the electric field the conductivity of a solution is the sum of the contributions to the current flow for each ion
This person pulls a crate 2.00 meters with a force of 120. N at an angle of 30.0 degrees to the direction of motion. The crate has a mass of 25.0 kg. How much work does the peron do on the crate?
w = Fdcos(theta) w = (120N)(2m)cos(30) w = 240(.87) w = 208Nm w = 208J
Superposition of Waves
waves can be added and subtracted here two waves combine involves: -constructive interference -destructive interference
Vibrations and Resonance SHM
waves-simple harmonic motion block on a spring pendulum resonance
Position
where you are -ex: 5 m from the door
Work Energy Principle
work done = change in kinetic energy
Hooke's Law and Compression
x < x(sub 0)
Hooke's Law and Tension
x > x(sub 0)
What do you buy from Penelec? Watts? (no)
you pay for kWh 7 to 10 cents per kWh kWh = killowatthour =killo (watt) hour =(1000)(watt)(3,600 seconds) =3,600,000 watt sec = 3.6 million Joules in energy a kWh is a unit of energy -it is used by power utilities because it is easy for them to do calculations with it, just multiply watts times hours.
Density
ρ = m/V Density of water at room temperature is about 1000kg/m^3 Whether we have a tiny droplet, ρ is rho (greek letter)
(italicized) P =
ρgh
Angular velocity
ω just like linear speed (velocity) is change in distance (displacement) per unit time. v = change in distance/change in time Angular velocity is the change in angle over change in time. ω(omega) = change in angle/change in time kinematic angular quantities are measure in s^-1 1 degree = 2pi/360 degrees
An 8.0 m radius merry-go-round completes one revolution every 7.0s. What is the angular velocity of the merry-go-round? With what speed are children moving when they ride on the merry-go-round? What is the centripetal acceleration these children feel when riding on the merry-go-round? What is the angular acceleration?
ω = change in angle/change in t ω = 2pi/7s = 0.89s^-1 2pi radians because it is a full revolution of a circle. v = rω v = 8.0m (0.89s^-1) v = 7.1 m/s a = v^2/r a = (7.1 m/s)^2/8m a = 6.3m/s^2 alpha = 0 because it is rotating at a constant speed.