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Physics 111 Fall 2017 Exam 3 cheat sheet
Oscillations about Equilibrium: Equation: Variables: Units: 𝜔 =
w: Angular frequency T: Period f: frequency w: rad/s T: seconds f: Hz (1/seconds) 𝐹 = −𝑘𝑥 F: Force exerted on a spring k: Spring constant x: displacement(distance a spring is stretched or compressed)
F: N
k: N/m x: m 𝑥 = 𝐴𝑐𝑜𝑠(𝜔𝑡) x: displacement or position of an object in oscillation A: amplitude w: angular frequency t: time x: m A: m w: rad/s t: seconds 𝑣 4 = −𝜔𝐴𝑠𝑖𝑛(𝜔𝑡) v: velocity of an object in oscillation A: w: t: v: m/s A: w: t: 𝑎 4 = −𝜔^8 𝐴𝑐𝑜𝑠(𝜔𝑡) a: acceleration of an object in oscillation A: w: t: a: m/s^ A: w: t: 𝜔 =
w: angular frequency of the oscillations of a mass attached to a SPRING k: spring constant m: mass w k: m: E = KE + PE E: Total mechanical energy KE: kinetic energy PE: Spring potential energy For all: Joules(Nm) 𝐸 =
𝑚𝑣^8 +
𝑘𝑥^8
E:
m: mass of the oscillator v: velocity of the oscillator k: x: displacement of the oscillator
E:
m: v: k: x: 𝐸 =
𝑘𝐴^8
E:
k: A: amplitude
E:
k: A:
Tips:
- Practice using the position, velocity, and acceleration equations
Don’t forget that
8
𝑚𝑣^8 +
= 8
= 8 𝑘𝐴^8 , this will be useful, and something that i’m seeing lots of people forget
- While it’s not on the equation sheet outright, remember that 𝑇 = 1 𝑓 this can be found using the first equation listed by cancelling out the 2p from both sides. This will be very useful, so try to remember this Waves and Sound: Equation: Variables: Units: 𝑣 =
v: speed of the wave propogation (if it is a sound wave, v is the speed of sound, 343 m/s l: wavelength (distance between peaks of the wave) T: period f: frequency v: l: meters T: f: 𝑣 =
v: F: Tension in the string/wire that the wave propagates along μ: linear mass density v: F: N μ: kg/m 𝜇 =
μ: linear mass density m: mass of the string/wire L: length of the string/wire μ: kg/m m: L: 𝐼 =
4 𝜋𝑟^8
I: Intensity of the sound P: power produced by the sound source A: The surface area of the wave propagation at the distance the observer is listening to the sound I: Watts/m^ P: Watts (J/s) A: m^ 𝛽 = 10 𝑑𝐵 ∗ log (
𝐼M
b: Sound intensity in decibels I: Sound intensity in W/m^ 𝐼M: Base sound intensity (constant) b: decibles I: Watts/m^ 𝐼M = 10 N=8^ 𝑤^ 𝑚^8 2 Doppler effect equations: 𝑓M: frequency heard by the observer 𝑓P: frequency produced by the source 𝑣M: velocity of the observer 𝑣P: velocity of the source
𝑓M:
𝑓P:
𝑣M:
𝑣P:
Fluids: 𝜌 =
𝜌: density m: mass V: volume 𝜌: kg/m^ m: V: 𝑃 =
P: pressure F: force A: area P: N/m^ F: A: 𝑃\W]\V = 𝑃 − 𝑃WX^ The gauge pressure is the pressure inside the body that you’re measuring (like a tire) minus the atmospheric pressure
P:
𝑃 8 = 𝑃= + 𝜌𝑔ℎ 𝑃 8 : Pressure at the bottom of a reservoir containing a fluid 𝑃=: Pressure at the top of a reservoir containing a fluid (atmospheric pressure) r: density of the fluid g: acceleration due to gravity h: height/depth of the reservoir
P:
r: g: h: 𝐹a]bcWQX = 𝜌de]fg𝑉𝑔 F: the buoyant force of an object in a fluid 𝜌de]fg: density of the fluid V: volume of the object submerged in the fluid
F:
V:
Conservation of mass: ∆𝑚: change in mass ∆𝑡: change in time r: density A: cross sectional area of the pipe or vessel through which the fluid is flowing v: velocity of the fluid flowing
r: A: v: Bernoulli’s Equation P: Pressure r: density v: velocity of the fluid flowing g: acceleration due to gravity y: the height of the fluid(for example, if the pipe water flows through turns upwards)
P:
r: v: g: y:
Tips:
- In the equation 𝑃 8 = 𝑃= + 𝜌𝑔ℎ, it is not necessarily a reservoir of water. It could be a gas, like Carbon Dioxide, or it could be a liquid, like oil. If there are multiple layers of fluid (like oil on top of water), You would find the pressure at the bottom if the oil, and that would become the new 𝑃=, before you find the pressure at the bottom of the water.
- In the buoyant force equation, the volume is the volume of the object that is under the surface of the fluid. So if the object is only partially submerged, only the volume that is under the fluid should be considered in this equation.
- In the conservation of mass equation, A is the cross sectional area of the pipe or other vessel through which the fluid is flowing. Remember the area of a circle is 𝐴 = 𝜋𝑟^8. This is worth memorizing for the exam. If you use the radius of the pipe instead of the area, you will get the wrong answer. Temperature and Heat: 𝑇i = (𝑇j − 32 )
𝑇i : Temperature in Celsius 𝑇j: Temperature in Fahrenheit 𝑇i : degrees Celsius 𝑇j: degrees Fahrenheit 𝑇n = 𝑇i + 273. 15 𝑇n: Temperature in Kelvin 𝑇i : 𝑇n: Kelvin 𝑇i : ∆𝐿 = 𝛼𝐿M∆𝑇 ∆𝐿: change in length 𝛼: coefficient of linear expansion 𝐿M: Original length ∆𝑇: Change in temperature
𝛼: 1/degree (of temperature) 𝐿M: ∆𝑇: ∆𝑉 = 𝛽𝐿M∆𝑇 ∆𝑉: change in volume 𝛽: coefficient of volumetric expansion (= 3 𝛼) 𝐿M: Original length ∆𝑇: Change in temperature
𝛽: 1/degree (of temperature) 𝐿M: ∆𝑇: 𝑄 = 𝑚𝑐∆𝑇 (^) Q: heat m: mass c: specific heat capacity (the heat required to change the temperature of the unit mass of a given substance by one degree) ∆𝑇: change in teperature Q: Joules m: grams c: Joule/gram*degree celsius ∆𝑇: 𝑄d]PfbQ = 𝑚𝐿d 𝑄d]PfbQ: Heat of fusion: the heat required to melt/freeze a substance m: mass of substance 𝑄d]PfbQ: Joules m: grams
