Liquid helium is stored at its boiling-point temperature of 4.2 K in a spherical container (r 0.30 m). The container is a perfect blackbody radiator. The container is surrounded by a spherical shield whose temperature is 77 K. A vacuum exists in the space between the container and the shield. The latent heat of vaporization for helium is 2.1 104 J/kg. What mass of liquid helium boils away through a venting valve in one hour?
PHYS 1010 Midterm Study Guide Scientific Method Hypothesis is used to predict the results of an experiment Repeated experiments verify or nullify the hypothesis "Code of ethics": scientists publish their results for review by other scientists It is impossible to completely prove a theory Repeatedly verified theories are called laws Bottomup method: science starts with evidence and facts and builds on those to create eventual theories Vectors and Coordinate Systems (Motion) Mechanics: deals with motion and the forces that cause motion Galileo developed the way we think about physical motion: the relationships between time, position, velocity, and acceleration Position and time We measure position by creating an arbitrary coordinate system/reference point around an object and describing the position as an (x, y) coordinate Vector: describes both magnitude and direction We add vectors "tip to tail" Breaking vectors into their x and y components simplifies adding Two vectors are equal if they have the same magnitude and direction, regardless of the starting points of the vectors Scalar: describes a magnitude of physical quantity (not a direction) Velocity: how fast an object is moving (speed and direction) Instantaneous velocity: velocity at a certain point in time Average velocity Acceleration: change in velocity with time Occurs with a change in magnitude or direction of the velocity vector Every object is accelerated by gravity at the same constant rate Throwing an object up in the air results in gravity decelerating the object until it reaches zero velocity, and then moving it back downward Projectile motion: moving up/down AND left/right Vertical acceleration doesn't affect horizontal velocity Forces Force: a push or pull that causes an object to accelerate Require an agent: something that acts to move the object Linear superposition of forces: multiple forces operating on an object, add forces together to solve for net force Application of force causes motion Inertia: the ability of an object to resist acceleration Newton's First Law: bodies at rest stay at rest, and bodies in motion stay in motion (unless acted upon by a force) No force = no change in velocity Newton's Second Law: force = (mass)(acceleration) Newton's Third Law: for every action, there is an equal and opposite reaction When two bodies interact, the force on the bodies from each other are always equal and opposite Weight: the measure of the force of gravity on a mass Apparent weight: a sensation evident when we are in an accelerating reference frame (ex. we feel heavier in ascending elevators) Gravitational force Weight is a magnitude of gravitational force Newton's Law of Gravity: the force of gravity between two objects depends on the mass of the two objects and the distance between them 2 Gravity near the earth's surface is constant (9.8 m/s ) because the distance between us, and the center of the earth, stays relatively constant Normal force: forces that balance gravitational force so that objects aren't constantly moving Always perpendicular to the surface Frictional force: force that opposes attempted motion Caused by the connecting and breaking of contact points when objects slide against one another Static friction occurs when two objects are not moving relative to each other, and opposes the initial motion Kinetic friction occurs when two objects are in motion relative to each other, and opposes the continuing motion Coefficient of friction: relates the normal force and frictional force Drag force: an opposing force that depends on the velocity of an object Occurs when an object moves through a fluid (gas or liquid) When drag force equals gravity, acceleration reaches zero and the object falls at a constant velocity (terminal velocity) Larger crosssectional area of object results in a higher drag force Tensional force: indirect force transmitted to an object by a string or rope attached to the object Pulling on the rope distributes force along the length of the rope and then accelerates the object Thrust force: occurs when an object propels itself without necessarily contacting anything externally When an object expels particles away from itself, the object experiences an equal and opposite reaction (Newton's 3rd Law of Motion) Electromagnetic forces: actionatadistance forces that arise from the presence and motion of electrons Nuclear forces: hold nuclei together and subsubatomic particles together Torque: a linear force that causes and object to rotate Only created if the force is perpendicular to the position vector Uniform circular motion: when the speed of an object moving in a circular path is constant Velocity is changing because direction is changing (so it is accelerating) Centripetal acceleration: causes curved path "Centrifugal" forces Not real according to Newton's laws As long as there is a normal force pushing on an object, it will not fall Rollercoaster example: nothing is holding cart on the loop, but the track is curving steeper than the cart would fall by itself Circular orbits: gravity working solely as a centripetal force Momentum Conservation laws: things aren't created or destroyed, but conserved Momentum involves mass (inertia) and velocity Force: change in momentum over some time span Linear momentum is conserved (no force = no change in momentum) Angular momentum: spinning momentum Conservation of angular momentum: angular momentum is the same throughout any period of time Decreased radius/size > faster spin Systems of particles Objects are made up of particles that don't always move in the same way We discuss systems of particles in terms of their center of mass (COM) COM: point that moves as though all of the mass were concentrated there and all forces were applied there The COM will follow the path as predicted for a single particle Allows us to discuss reallife systems without describing every particle in the object individually Impulse force: force that is exerted after elastic bonds between particles contract upon collision Longer collision > smaller force Energy and Work Energy: a scalar quantity associated with the condition of one or more objects Kinetic energy: energy from the motion of an object Work: energy transferred to or from an object by means of force acting on an object Changing energy = work = (force)(displacement) A force is necessary to change motion Positive work: energy transferred to an object Negative work: energy transferred from an object Potential energy: the energy an object has due to position "Stored" inside an object Change in kinetic energy Conservative and nonconservative forces Upward and downward forces of an object thrown upward have the same speed and kinetic energy. Therefore, the kinetic energy is "conserved" when dealing with gravitational force A "conservative" force will return the work it does on an object when the object is turned to its original position Gravitational force is conservative and frictional force is non conservative Conservation of mechanical energy Mechanical energy = kinetic energy + potential energy Kinetic energy and potential energy tradeoff but total mechanical energy stays the same Thermal energy: motion causes heat Heat: change in temperature that occurs when thermal energy is transferred between to touching objects Positive when energy is transferred to an object from the environment Negative when object loses thermal energy to the environment Always transferred from the hotter object to the colder object Heat transfer Radiation: heat from light Conduction: heat transferred because a hot object touches a cold object Convection: heat transfer by motion of fluid: heated fluid moves away from the object, carrying heat with it Absorption of heat Heat capacity: the amount of energy required to heat up an object Specific heat: heat capacity per unit mass of a substance Metal conducts heat very well; insulating materials like fiberglass and Styrofoam trap air and hold it in place to keep things cool Air almost doesn't conduct heat Thermal expansion: adding kinetic energy to a solid lattice causes atomic bonds to stretch and leads to an expanding of the entire lattice The way we measure temperature Overstretching > change in state of matter Temperature: used to describe a measure of heat Lowest possible limit is 0K when atoms stop vibrating Matter cannot exist below 0K Work done on a system by an external force External forces can do work on a closed system by transferring energy to or from a system Work done against friction becomes thermal energy (heat) Work done against the force of friction is the loss of mechanical energy to thermal energy Conservation of energy: the total amount of energy in a closed system can never change Earth is not a closed system, but universe is Laws of Thermodynamics 0th Law: if objects A and B are each in thermal equilibrium with a third object C, then objects A and B are in thermal equilibrium with each other If something is in one part of a system, then it is in all parts of the system 1st Law: the difference between the transferred thermal energy and change in mechanical energy determines the change in the internal energy of the system 2nd Law: the entropy of a closed system can never decrease 3rd Law: in order to cool something to 0K, you need something colder than 0K, which can't exist as matter. Therefore nothing can be cooled to 0K Entropy: randomness/disorder Many natural processes are irreversible (not symmetric) Problematic because conservation of energy is symmetric and doesn't suggest any kind of direction If an irreversible process occurs in a closed system, the amount of entropy always increases (it can never decrease) Change in entropy is thought to be a factor in our concept of the "arrow of time" Time moving backwards would violate the concept of entropy Heat engines and refrigeration When a hot object and cold object are touching, energy moves from the hot object t the cold object, and we can siphon off that energy as it moves and use it to drive an engine Efficiency is never 100% because some heat must flow to the cold object; however, the energy being transferred to the cold object doesn't do us any good Refrigerators go from hot to cold fridges are just reversing the previous flow of energy. We need a heat engine as well as the cooling system Electric Charge Particles have either a positive or negative charge Negatively charged: object contains more negative particles than positive particles Positively charged: object contains more positive particles than negative particles Electrically neutral: object contains equal amounts of positive and negative particles Nature prefers neutral charges The terms "positive" and "negative" don't mean anything; they just refer to the fact that the charges are opposite Electrostatic/electric force: the force that charged particles exert on each other Objects with the same electrical charge repel each other, while objects with opposite electrical charges attract each other Strong electrical charges can induce an opposite charge in a neutrally charged system Grounding can neutralize a system’s charge Grounding: touching an object to the ground (the earth is so big that it can absorb any extra charge without problem) Current: rate at which charge moves past a given point in a given amount of time Charge is quantized (comes in basic units based on electrons that cannot be divided) Charge is conserved (cannot be created or destroyed, only moved around) Charge moving through materials Conductors allow electrons to move freely (ex. metal) Everything can be a conductor with enough electricity Resistance inhibits flow Ohm's law: as potential increases, current increases, and when resistance increases, current decreases (v = IR) I is current, R is resistance, V is voltage Insulators don't allow electrons to move as freely Semiconductors are somewhere in between Superconductors allow charge to move without hindrance Coulomb’s law: force exerted by charged particles on each other depends on the size of the charge of the particles as well as their distance from one another * Increasing force means opposite charges (attracting particles) Electric fields: electrostatic forces existing around a charged particle We draw electric field using field lines Field lines closer together shows stronger force (flux) Field lines extend away from positive charges and toward negative charges Charged particles have potential energy Electric potential (voltage): potential energy per electrical charge Electric current: flow of electrons in motion (negative to positive) Inserting battery into loop of conductive material creates a flow Series Circuits Battery/power supply: creates a difference in potential energy Path from one end of battery to another (wire or other conductive material) > Electric current Electrons pushed through a resistor, which slows the current down/steals kinetic energy from the electrons to power a machine Power multiple machines by adding multiple resistors to circuit around the circuit Each resistor increases the overall resistance of circuit Parallel circuits Put resistors into a circuit next to each other, creating multiple paths for the electron to move through If one of the paths slows down (because electrons have to slow to enter the resistor), the backedup electrons move through the next parallel resistor Adding resistors decreases the resistance of the circuit, increasing current flow (like adding lanes to a highway) Too fast of a current is an issue because wires can only hold so much electricity Direct current (DC): current that flows in only one direction Usually used in electronics/devices Alternating current (AC): current alternates direction (60 times/s (60 Hz)), which changes faster than what we can see (20 Hz) Easier to generate and travel over long distances Argument between Tesla (AC) vs. Edison (DC) because AC is dangerous Edison created the electric chair, which used AC Transformers are used to change between AC and DC Magnetism Magnetic fields Magnetic particles are dipoles, and the two poles of a magnet are the North and South poles All magnetic field lines originate from the North Pole and move toward the South Pole We draw magnetic field lines by placing a compass near the magnet and tracing the direction in which the arrow of the compass points (towards the south magnetic pole) Right now the south magnetic pole is at the North Pole of the Earth Earth's poles have switched historically Earth's magnetic poles are not exactly located at the north and South Pole Field lines pass through the magnet and form closed loops Opposite magnetic poles attract each other, and like magnetic poles repel each other Northern lights: magnetic fields crashing down in one place Spin: some particles, like electrons, produce a magnetic field characteristically Permanent magnet: magnetic fields of many particles arranged in a specific manner Some materials let particles float and when they go close to a magnet, the particles will arrange in a way that creates a magnet out of that material Magnetic force only affects moving particles The equation for a magnetic field Tells us which direction the force will accelerate the charged particle (perpendicular to both the direction of the velocity and the magnetic field) Shows that magnetic fields tend to make particles move in a circle Magnetic fields can never increase the kinetic energy of a moving particle, only change the direction Magnetic fields cannot do work * Magnetic fields only exert force on moving charged particles (moving charge is the same as an electric current) Magnetic force on a currentcarrying wire Running a current through a wire and putting it in a magnetic field will make the wire move back and forth Electrical current produces a magnetic field Loop of current inside a magnetic field is an electric motor: converts electrical current into mechanical energy Works by alternating the magnetic field/current direction Solenoid: wire wrapped in a cylindrical shape to amplify the magnetic field Solenoids start car engines (magnetic field exerts a force that pushes a button that starts the car) Toroid: a solenoid with ends connected to form a donut Create an amplified magnetic field that force charged particles to move in a circular path Used as particle accelerators Magnetism: moving electricity/charge Magnetism creating electricity "Induction": inducing an electric field Magnet being moved into a loop of wire creates electric current because from the magnet's perspective, those particles are now moving Electricity causing electricity Putting a loop of current next to another loop of current creates induction > Wireless communication Lenz's law Current of a wire inserted into a magnetic loop will induce magnetism that is the opposite direction of the original magnet, so it will "push back" at the magnet being inserted Verifies that there are forces being created, and forces can do work Dropping a magnet through a copper pipe Copper conducts electricity Changing magnetic fields create electricity Current/magnetic field in pipe pushes against magnet (Lenz's law), so the magnet slows down as it falls through pipe Electromagnetism Electricity and magnetism are basically the same thing, they just work in opposite directions Induction and energy transfers Rail guns: conducting wire frame creates magnetic field that pushes one side of moving wire out and gets bigger and bigger; used to fire projectiles Eddy Currents: "whirlpool" currents produced when a solid object moves through a magnetic field Result in lost energy Useful for train brakes Eddy currents created by superconductors create gigantic electric currents with no resistance > huge magnetic field > maglev trains Superconductors only conduct at low temperatures, which is an issue because it's lower than the temperature of liquid nitrogen (used to cool it off); superconductors are difficult to keep cold all the time, which is why we don't use them for everything Maxwell's equations All of these equations together explain everything about electricity and magnetism 1. Definition of electric field 2. Definition of magnetic field 3. Faraday's law: a changing magnetic field creates an electric field 4. AmpereMaxwell Law: a changing electric field creates a magnetic field Explanation that electromagnetic radiation means that light is made up of waves But waves must travel through a substance so how does light travel through space According to Maxwell, light is electricity and magnetism (a wave that doesn't need to travel through anything) Electromagnetic waves Maxwell's equations 3 and 4 explain that light can move through an empty space because it is creating/driving itself with electricity and magnetism Pushing electric charges up and down creates electric waves/electric field which creates a magnetic field, and on and on We can send signals (radio, etc.) that keep moving forever The speed of light is a constant (never changing) Throwing a baseball 20mph means the speed it 20mph Throwing a baseball 20mph out a car while driving 20mph means the speed is 20mph Turning a flashlight on means the speed is constant, but turning a flashlight on while running also results in a constant speed Concept of mass/time/length units is called into question, changes everything we know about physics