Show:
Waves and Oscillations
Energy, Gravity, and Statics
Rotational Motion and Simple Harmonic Motion
Fluids and Momentum
Thermodynamics
100
What is a wave?
Energy transported by some medium in the form of oscillations
100
(a) What is the conceptual definition of kinetic energy? (b) What is the conceptual definition of potential energy? (c) What is the conceptual definition of mechanical energy?
(a) Energy of motion (b) Energy of potion/arrangement (c) Total energy of a system
100
(a) What the units of rotational translation and what makes them unique? (b) How are these rotational units related to meters?
(a) Radians (or degrees) and they are "unitless" (b) They are related by the radius of the circle/path length of the oscillation
100
What are the units of Bernoulli's equation and how are they related to units of energy?
Units of pressure [Pa] and is actually [J/m^3], i.e. energy per unit volume
100
What is the ideal gas law? Label and give units for every symbol in the equation
PV = nRT -- P = pressure [Pa] -- V = volume [m^3] -- n = number of moles [moles] -- R = gas constant [N/moles*K] -- T = temperature [K]
200
How are position (trajectory), velocity and acceleration of an oscillating object related?
Velocity is the derivative of position, and acceleration is the derivative of velocity.
200
(a) Besides the fact that one conserves energy and the other does not, what differentiates a conservative from a non-conservative force? (b) Name two conservative forces (c) Name two non-conservative forces
(a) Conservative forces have potential energy associated with them (b) Spring force, gravity (c) Applied force, friction, air resistance
200
On a racetrack, why are the turns "banked"? What determines the maximum bank the turn should have? What determines the minimum?
Normal force contributes to centripetal force. Max bank for max a_c (i.e. max v), min bank for min a_c (i.e. min v).
200
What is impulse and how is it related to momentum?
dp = F*dt. A force applied over some time gives a change in momentum
200
Give a microscopic description of P, (N/V), and T in the ideal gas law
P = momentum transfer per second N/V = number density of molecules T = mean kinetic energy
300
What produces beats? How does one determine beat frequency?
Two different frequencies interfering. Fb = |f1 - f2|
300
What differentiates the mechanical energy of an object IN orbit and an object NOT in orbit?
Mechanical energy is negative for a bound orbit
300
(a) What is the total work done during one cycle of simple harmonic motion? (b) Can non-conservative forces do simple harmonic motion?
(a) Zero (b) No
300
How does a vacuum work?
Pressure difference (against atmosphere) applies a net force on whatever the vacuum is near
300
(a) What is the First Law of Thermodynamics? Define each symbol in the formula (b) How is change in a thermodynamic system's energy related to its change in temperature?
(a) U = Q - W -- U = change in internal energy of the system -- Q = Heat transferred to the system -- W = work done by the system (b) Change in energy is proportional to change in temperature, scaled by the specific heat
400
What is the solution to the wave equation? Label all quantities in the solution and define them in terms of the wavelength [lambda] or frequency [f].
y(t) = Asin(kx - wt) -- A is the amplitude -- k is the wave number (2pi/lambda) -- x is spatial displacement -- w is the angular frequency (2pi*f) -- t = time
400
(a) What two conditions must be satisfied for a static system? (b) How do I choose where to put my pivot point in a statics problem?
Zero net force, zero net torque
400
How many initial conditions do we need to get the particular solution to the harmonic oscillator? What are these conditions? What is the "phase shift" of an oscillating system?
Two conditions: initial velocity and initial position. Phase shift is how much the sine wave is shifted to accommodate initial condition.
400
Archemedes Principle is a clever trick... What force is it encoding/describing (i.e. what is Buoyant force actually)?
The net fluid pressure on an object, i.e. pressure difference between the top and bottom of the object
400
Heat is a nebulous concept with a very specific definition. What is the formal definition of heat?
Heat is any change in internal energy that is not work
500
Given the formula for the Doppler Formula f' = [(v +/- u_o)/(v +/- u_s)]f, how do you determine the positive or minus sign?
- over + for moving towards and + over - for moving away
500
When an object leaves the earth at escape velocity, does it matter what trajectory it takes to get to infinity? If so, which trajectory should it take and why? It not, why not?
It doesn't matter! PE only depends on radial distance, not angular position!
500
1) What method do we use to get a harmonic oscillation equation for an oscillating system? 2) What is the flaw in this method? 3) How do we "remedy" this flaw?
1) Newton's Second Law 2) There is no minus sign in our SHM equation when there needs to be! 3) We just put the minus sign in.
500
(a) Why do we not take atmospheric pressure into consideration in any of our calculations? (b) Why is it harder to breathe in Denver than in Boston?
(a) It pushes in every direction the same amount (b) Air is less dense in Denver. The atmosphere is not an ideal gas!
500
What are the four thermodynamic processes and how are they defined? If you can't remember the exact terminology, just the description is okay
-- Isothermic: constant temperature -- Isochoric: constant volume -- Isobaric: constant pressure -- Adiabatic: No heat transfer