
Units
Newton's laws
Circular motion
Friction
Spin
Pressure
Physics challenge questions (A level)
Astronomy challenge questions (A level)
Astronomy
Order of magnitude problems
A "*" indicates a link to a solution.
Artificial gravity Launch cost Bamboo Light travel time Sunlight mass Visual resolution Earth equatorial centripetal acceleration Dinosaurs Pinatubo Rice Earth temperature Age of the universe Strength of gravity Death Star
Artificial gravity de Broglie wavelength Launch cost Bamboo Death Star Sunlight mass Visual resolution Cosmic ray muons Photon momentum Relativistic velocity addition Cold atoms Rice Earth temperature Age of the universe Strength of gravity Death Star Dark matter
Without using any kind of measurement device, try estimating things like mass and length for various objects. If you don't have the object handy, imagine it in your mind. For the following objects, what is
Height of a 2 liter bottle of Mountain Dew.
Diameter and mass of a quarter, a ping pong ball, a tennis ball, and a soccer ball.
Balls.
Coins
Distance between two train tracks.
Distance between Manhattan streets, such as from 42nd Street to 43rd street.
Length and width of Central Park. (Central Park extends from 59th Street to 110th Street
and from 5th Avenue to 8th Avenue).
Length of Manhattan Island.
Height of Tyrion Lannister.
Height of the letters on a stop sign and the distance between opposite edges of the sign.
Length and width of a standard sheet of paper.
Diameter of a light on a stoplight.
Answers
What is the mean distance from the sun to the Earth, what is the speed of light, and how long does it take light to cover this distance?
Speed of the New Horizons spaceship = 14.5 km/s Speed when it passed Pluto Distance to Pluto = 39 Astronaumical Units Distance to Alpha Centauri = 4.4 light years The nearest starAt New Horizon's present speed, how long does it take to travel 39 astronaumical units and 4.4 light years?
The Virgo cluster of galaxies is 54 million light years away and is moving away from us at 1254 km/s. At this speed, how many billion years does it take the cluster to cover a distance of 54 million light years? This is an estimate of the age of the universe.
Most beer bottles are 12 ounces in volume and 5 percent alcohol by volume. Define one "Bond" to be the volume of alcohol in one bottle of beer. How many mL of alcohol is one Bond?
Wine is typically 13% alcohol and Scotch is typically 40%. How many ounces of wine or Scotch correspond to one Bond of alcohol?
How many Bonds of alcohol are in a 750 mL bottle of wine, a 750 mL bottle of Scotch, and a 15.5 gallon keg of beer?
Using Wikipedia, find the diameter, thickness, and mass of a penny and calculate its density.
A penny is 2.5% copper and 97.5% zinc. The density and price/kg of these metals is
Density Price/kg g/cm3 $/kg Zinc 7.14 2.0 Copper 8.96 6.2 Gold 19.3 43000What is the cost of the metal in a penny?
What is the price of a penny made of gold?
In the "Fight Science" youtube video "Wushu Master vs. Snake" the strike of a wushu master and a snake are measured.
Distance Time (inches) (ms) Wushu master 15.5 94.7 Snake 4.65 29.5If constant acceleration is assumed, what is the acceleration and final speed for each strike? (Use units of meters and seconds).
In this scene from the film "A Team", a tank fires a shell to use the recoil for propulsion.
TankRecoilSpeed * TankMass = ShellSpeed * ShellMassUsing data from the web, what are typical values for TankMass, ShellSpeed, and ShellMass? What would you estimate is the recoil speed of the tank?
Starting from the point when the tank is dropped from the plane to the point where it reaches the lake bottom, plot the height, vertical velocity, and vertical acceleration as a function of time.
A 3 meter long cannon with a mass of 2000 kg fires a 10 kg cannonball
at speed of 600 meters/second. What is the recoil speed of the cannon?
What is the average acceleration of the cannonball while it is in the barrel?
Solution
A punter kicks a ball with a vertical velocity of 30 meters/second and a horizontal velocity of 20 meters/second. For how long is the ball in the air and how far horizontally does it travel before it hits the ground? Assume zero air drag.
Chuck Norris has a mass of 110 kg and he has a jet pack that generates 1800 Newtons of upward force. He is also on the surface of the Earth and subject to Earth gravity, which we shall assume to be 10 meters/second^{2}.
What is his vertical acceleration?
Solution
Chuck has a mass of 110 kg. How much gravitational potential energy does he
gain if he climbs a 12 meter staircase in 5 seconds, and what is the power in Watts?
Solution
Speed of a baseball pitch thrown by Randy Johnson 45 meters/second Initial height of the baseball 2.2 meters Distance from the pitcher to the batter 20 metersThe pitch is thrown horizontally so that if there were no gravity, it would travel horizontally and stay at a height of 2.2 meters. If gravity is included, how much does the pitch drop vertically when it arrives at home plate?
Climb a set of stairs as fast as you can. Measure the height of the stairs and the time required to climb them and calculate the power.
Obtain a youtube video of any of the following:
A Usain Bolt 100 meter sprint
A Formula1 car accelerating from 0 to 75 m/s.
A drag racing car accelerating from 0 to 100 m/s.
A cheetah accelerating from 0 to 20 m/s.
Analyze the video framebyframe to generate a plot of position vs. time and use it to estimate the velocity and acceleration vs. time.
Plot the power vs. time, where
Power = Force * Velocity = Mass * Acceleration * Velocity
The Earth has a radius of 6371 km. What is the speed of the equator due to the Earth's spin, and what is the corresponding centripetal acceleration?
Mass of Earth = 5.972⋅10^{24} kg Radius of Earth = 6372 km Gravity constant = 6.674⋅10^{11} Newton meters^{2}/kg^{2} Surface gravity = 9.807 meters/second^{2}The space station is at a height of 400 km above the surface of the Earth. What is the gravitational acceleration at this height?
What is the orbital velocity at an altitude of 0 km and 400 km?
What is the gravitational potential energy of a 1 kg object 400 km above the surface of the Earth?
What is the kinetic energy of a 1 kg mass orbiting at an altitude of 400 km?
What is the cost of electricity in Joules/$?
What is the electricity cost to propel an object at orbital velocity at an altitude of 400 km?
Using Wikipedia, how much $/kg does it require to launch material into space? Find data for several rockets.
Suppose you are on a ship in the middle of the ocean. How far can you see a floating buoy as a function of your height above the ocean surface? Express the answer as
Radius of the Earth = R = 6371 km Height above the ocean surface = H Distance for which you can see a buoy = D = C H^{½} km
Use the approximation that H << R.
In space, artificial gravity can be generated by spinning the spaceship. NASA experiments show that the spin period has to be 30 seconds for the astronauts to not get dizzy. If a spaceship has a spin period of 30 seconds and if the artificial gravity is 10 meters/second^{2}, what is the spin radius?
A 800 kg car has an infinitely powerful engine and the tires have a coeffient of
friction of 1.4. What is the maximum acceleration?
Solution
Radius of curvature = 8 meters Tire coefficient of friction = .9 Car mass = 1300 kgWhat is the maximum cornering speed? Solution
A soccer ball with a radius of .11 meters rolls with a speed of 20 m/s. What is the spin frequency and the angular velocity?
$\theta 2$ = Angular velocity Ek = Kinetic energy = .5 M V^{2} Es = Spin energy = .5 I $\theta 2$ Et = Total energy = Ek + EsWhat is Ek/Et?
Suppose a ball rolls without slippling down a ramp.
H = Initial height of the ball g = Gravity constant V = Velocity of the ball when it reaches the bottom of the rampWhat is V?
A billiard ball with a radius of 30 mm rolls with a speed of 3 meters/second. What is the ball's spin rate in revolutions per second and radians per second?
Suppose a football receiver with a vertical leap of .8 meters jumps and catches a ball at the top of the leap.
V = Velocity of the ball = 20 m/s Mb = Mass of the ball = .42 kg M = Mass of the football player = 100 kgWhat is the recoil velocity of the receiver?
How long does it take the receiver to drop .8 meters after catching the ball?
How far is the receiver knocked horizontally by the recoil?
Suppose the receiver catches the ball far from his body so that the recoil also delivers angular momentum. If the ball is caught 1 meter from his axis of rotation, how much angular momentum does the ball deliver?
If the receiver has a moment of inertia of 2.5 kg m^{2}, what is his spin frequency after catching the ball?
Position Mass (meters) (kg) Chuck Norris 11 110 Tyrion Lannister 15 60Where is the center of mass?
M = Mass of the Earth = 5.97e24 kg R = Radius of the Earth = 6371 km m = Mass of the moon = .0123 M r = Radius of the moon = .273 R D = Distance from the Earth to the moon = 60.3 R L = Distance between the center of mass of the Earth and moon and the center of the EarthWhat is L/D?
If we assume that the Earth and moon are spheres of uniform density, what is
Angular momentum of the Earth's spin?
Angular momentum of the moon's spin?
Angular momentum of the moon's orbit around the Earth?
Using data from the web, what is a typical speed and spin rate for the following balls? Measure spin rate in revolutions per second.
A baseball curveball.
A golf ball hit by a driver and a 9 iron.
A tennis groundstroke hit with extreme topspin.
A ping pong ball hit with extreme spin.
A football thrown with an extreme spiral.
A soccer ball kicked with extreme speed and spin.
Diameter Mass Density (mm) (g) (g/cm^{3}) Ping pong 40 2.7 .081 Squash 40 24 .716 Golf 43 46 1.10 Badminton 54 5.1 .062 Racquetball 57 40 .413 Billiards 59 163 1.52 Tennis 67 58 .368 Baseball 74.5 146 .675 Whiffle 76 45 .196 Football 178 420 .142 Rugby 191 435 .119 Bowling 217 7260 1.36 Soccer 220 432 .078 Basketball 239 624 .087 Cannonball 220 14000 7.9 R = Ball radius F = Spin in revolutions per second V = Ball velocity Ve = Velocity of the edge of the ball due to its spin = 2 Pi R F Z = Spin ratio = Ve/VFor a ball rolling on the ground, Z=1.
Calculate Z for the data you collected.
Suppose a bowling ball slides along the floor with zero spin and then friction causes the ball to start spinning.
V = Initial speedWhat is the speed of the ball once it starts rolling smoothly?
The Earth's moon was formed from the debris of a giant collision. After the collision, any material within the Earth's Roche radius formed a ring and then fell back to the Earth. Material outside the Roche radius coalesced into the moon. If angular mometum is conserved as the moon spirals outward, then what was the spin period of the Earth when the moon was located at the Roche radius?
This sets the characteristic height of the atmosphere.
If an asteroid hits the Earth with a speed of 20 km/s and a density of 2 g/cm^{3} and all of its kinetic energy goes into heating the atmosphere, what size asteroid is required to heat the atmosphere by 100 Kelvin?
Draw a diagram showing how to make Plutonium239 from Uranium238.
What is the approximate lifetime of a virtual electron?
The formula for relativistic velocity addition is:
Speed of light = C Velocity of a spaceship = V_{S} Velocity of a cannonball fired by the spaceship = V_{C} (In the frame of the ship) Velocity of the cannonball in the rest frame = V_{R} = (V_{A} + V_{B}) / (1 + V_{A} V_{B} C^{2})If a spaceship moving at .5 C fires a cannonball at a speed of .5 C (with respect to the ship), what is the speed of the cannonball in the rest frame?
M = Mass of a gas molecule = 1.4e25 kg for a rubidium atom V = Characteristic velocity of gas molecules E = Mean thermal energy of gas molecules = .5 M V^{2} k = Boltzmann constant = 1.38e23 Joules/Kelvin T = Temperature W = Quantummechanical wavelength Q = Characteristic momentum of a gas molecule = M V h = Planck constant = 6.62e34 Joules seconds = Q WFor a gas in thermal equilibrium, each degree of freedom has mean energy .5 k T. For motion in 3D there are three degrees of freedom and so
E = .5 M V^{2} = 1.5 k TAtomic cooling experiments can reach temperatures of ~ 10⋅10^{7} Kelvin. For this temperature, what is the quantummechanical wavelength of a rubidium atom?
Particle wavelength = W Speed of light = C = 2.998⋅10^{8} meters/second Planck constant = h = 6.626⋅10^{34} Joule seconds Particle momentum = Q Particle velocity = V Particle frequency = F Particle mass = M De Broglie formula: h = Q W Wave formula: V = F W Compton wavelength W = h/(MC)
The Compton wavelength is the wavelength of a particle that is "barely relativistic", where we assume Q = M C. This sets the range of forces delivered by virtual particles. For example, the strong force is delivered by pions and its range is equal to the Compton wavelength of a pion.
What is the wavelength of a baseball moving at 40 m/s?
What is the wavelength of an Xray with an energy of 10000 electron Volts?
What is the wavelength of an electron with an energy of 10000 electron Volts?
What is the frequency of a green photon with a wavelength of 555 nm?
What is the speed of a proton and an electron with a kinetic energy of 5 MeV?
What is the Compton wavelength of an electron, a proton, a pion, and a Higgs boson?
Reference: www.jaymaron.com/particles/particles.html
Bamboo is a fastgrowing tree. Using Wikipedia, how much wood can 1 km^{2} of bamboo forest produce per year and much energy is released from burning 1 kg of bamboo? How much energy is used by civilization in one year and how many kg^{2} of bamboo forest does it take to equal it?
The Earth's orbit radius is 1.5e11 meters and the orbit time is one year. Calculate the Earth's orbit velocity in meters/second.
What is the distance from Earth to Mars when they are as close as possible?
How long does it take light to travel this distance?
How long does it take a spaceship traveling at 10 km/s to cover this distance?
If a sprinter covers 40 yards in 4.4 seconds then what is the average speed in meters/second?
Convert 65 miles/hour to meters/second, showing the steps in the conversion.
Distance to Alpha Centauri = 4.4 light years The nearest star Speed of the New Horizons spaceship = 14.5 km/s Speed when it passed PlutoAt New Horizon's present speed, how long will it take to travel 4.4 light years?
How much CO2 was released by the Pinatubo volcano and what was the volume of magma ejected?
What is the mass of CO2 in the Earth's atmosphere and how many Pinatubos would it take to double the atmosphere's CO2?
Using data from Wikipedia,
How many kg of water does it take to grow one kg of rice?
How many Calories are in 1 kg of rice?
Approximately how many Calories you eat in one day and one year?
How many Joules are there in one food Calorie?
How many Joules do you require in one year?
How many kg of rice do you require in one year?
How much water does it take to grow a year's worth of rice?
How many kg of water flow through the Mississippi per year?
If all of the water in the Mississippi is used to produce rice, how many people
can the Mississippi support?
Energy in one day = 2500 Calories/day Energy in one Calorie = 4200 Joules/Calorie Energy in one day = 10.5 MJoules/day Energy/Mass of rice = e = 15 MJoules/kg Mass of rice in one day = m = .7 kg/day Mass of rice in one year = M = 256 kg/year Water footprint of rice = w = 1000 kg water per kg rice Water for 1 year = W = M w = 2.56e5 kg/year Mississippi flow rate = F = 1.67e7 kg/second = 5.0e14 kg/year People supported = N = F/W =1.95e11 people = 195 billion people
Using Wikipedia, what is the $/kg required to launch material from the surface of the Earth into low Earth orbit? Find data for several rockets.
B_{1} = Brightness of Pluto in Watts/meter^{2} when it is 30 AU from the sun B_{2} = Brightness of Pluto in Watts/meter^{2} when it is 40 AU from the sunWhat is B_{1} / B_{2}?
Mass of the Earth's atmospere = M = 5.15e18 kg Surface area of the Earth = A = 5.10e14 m^{2} Gravitational constant = g = 9.8 m/s^{2} Pressure of Earth's atmosphere = P = 101000 Pascals = M g / A = 15 pounds/inch^{2} = 1 Bar Mass above one meter^{2} of surface = m = M / AOne bar is defined as the Earth's mean atmospheric pressure at sea level
Properties of atmospheres:
Density Pressure m Gravity (kg/m^{2}) (Bar) (tons/m^{2}) (m/s^{2}) Venus 67 92.1 1050 8.87 Titan 5.3 1.46 109 1.35 Earth 1.22 1 10.3 9.78 Mars .020 .0063 .54 3.71 Mass of atmosphere above one meter^{2} of surface = m = 10.3 tons for the Earth P = m gYou don't need a pressure suit on Titan. You can use the kind of gear arctic scuba divers use. Also, the gravity is so weak and the atmosphere is so thick that humanpowered flight is easy. Titan will be a good place for the X games.
Pandora is the moon in the film "Avatar". Using data from the web, add Pandora to the above table.
Suppose an asteroid is a sphere of uniform density
Mass of a sphere = M Radius of a sphere = R Density of a sphere = D = 2000 kg/meter^{3} (rock) Gravity constant = G Gravitational energy of a sphere = E_{grav} = .6 G M^{2}/R Energy of a hydrogen bomb = E_{bomb} = 4e16 Joules (equivalent to 10 Megatons of TNT)For what value of R is E_{grav} = E_{bomb}?
In Star Wars, a death star destroys planet Aldebaran. Suppose we assume that the death star is powered by antimatter.
Mass of antimatter = M_{anti} Speed of light = C = 3.00e8 meters/second Energy in antimatter = E_{anti} = M C^{2} Mass of the Earth = M = 6.0e24 kg Radius of the Earth = R = 6371 km (From Star Wars) Density of the Earth = D = 5500 kg/meter^{3} Gravitational energy of the Earth = E_{Earth} = .6 G M^{2} / R (Assume a uniform density)For what value of M_{anti} is E = E_{anti}?
MicroWatts Half life Mantle PicoWatts/kg /kg (billion abundance of mantle years) (ppb) Uranium238 94.6 4.47 30.8 2.91 Uranium235 569. .70 .22 .125 Thorium232 26.4 14.0 124 3.27 Potassium40 29.2 1.25 36.9 1.08 Total 7.38The Earth loses heat at a rate of .087 Watts/m^{2}, for a global heat los of 4.42e13 Watts.
80% of the Earth's heat is from radioactivity and 20% is from accretion.
For radioactivity,
Time elapsed = T Half life of the material = T_{half} Original mass of material = M_{0} Mass of material left after time T = M = M_{0} exp(T/T_{half})Based on the above data, what will be the radioactive intensity of the Earth in PicoWatts/kg one billion years from now?
Matmos = Mass of the Earth's atmosphere Fatmos = Mass fraction of nitrogen in the Earth's atmosphere Mnitro = Mass of nitrogen in the Earth's atmosphere Area = Surface area of the Earth Density = Density of the Earth's crust = 2000 kg/m^{3} (This is approximate. It varies from 1500 to 3000) Fcrust = Mass fraction of nitrogen in the Earth's crust Depth = Depth below the surface of the Earth Mcrust = Mass of the Earth's crust down to a depth "Depth" = Area * Depth * Density Mnitro = Mass of nitrogen in the Earth's crust down to a depth "Depth" = Mcrust * FcrustUsing wikipedia, what are the values of the above numbers?
For what value of "Depth" is Matmos = Mnitro?
Composition of the Earth's crust.
Parts per thousand Oxygen 460 Silicon 270 Aluminum 82 Iron 63 Calcium 50 Magnesium 29 Sodium 23 Potassium 15 Titanium 6.6 Hydrogen 1.5 Manganese 1.1 Phosphorus 1.0 Fluorine .54 Barium .5 Carbon 1.8 Strontium .36 Sulfur .42 Zirconium .13 Tungsten .0011 Vanadium .19 Chlorine .17 Chromium .14 Rubidium .06 Nickel .09 Zinc .079 Copper .068 Cerium .060 Neodymium .033 Lanthanum .034 Yttrium .029 Nitrogen .020
Humans generate energy by reacting hydrocarbons with oxygen. Consider the reaction of octane, which has 8 carbons and 18 hydrogens.
C_{8}H_{18} + 25 O_{2} > 9 H_{2}O + 8 CO_{2} M_{octane} = Mass of octane in the reaction M_{oxygen} = Mass of oxygen in the reactionWhat is M_{octane} / M_{oxygen}?
How long does it take light to travel this distance?
How long does it take a spaceship traveling at 10 km/s to cover this distance?
R = Radius of an asteroid P = Probability per millenium of a hit from an asteroid at least as large as RUsing data from the web, what is P for R = .01, .1, 1, 10 km?
How many stars are there in the Milky Way?
How fast is the Milky Way moving with respect to the cosmic microwave background radiation?
What is the heat capacity of air and what is the mass of the Earth's atmosphere?
If an asteroid hits the Earth with a speed of 20 km/s, a diameter of 10 km, and a density of 2 g/cm^{3}, and if all of its kinetic energy goes into heating the atmosphere, by how many degrees Kelvin does the temperature of the atmosphere rise?
How many Watts of sunlight strike the Earth?
If the Earth were an ideal blackbody with uniform temperature, what is the blackbody radiation power?
Setting the above two quantities equal, what is the resulting temperature of the Earth?
What are the fusion reactions that convert hydrogen to helium in the sun? Using Wikipedia, what is:
Mass of 4 protons = m Mass of a helium nucleus = M Fraction of mass converted to energy = F = (Mm)/MUsing E=MC^{2}, how much energy is released in the fusion of 1 kg of hydrogen into helium?
What elements would we have to bring from Earth if we want to grow crops on Mars?
What biochemical processes are the same for all Earth life forms?
In Copernicus' time, what astronomical evidence was consistent with the heliocentric model and what evidence was consistent with the geocentric model? (It's possible for evidence to be consistent with both)
What discoveries did Galileo make that relate to heliocentrism? How is each discovery inconsistent with geocentrism?
Describe the life cycle of a star that ends its life as a neutron star.
Draw a timeline of the universe and the Earth, starting from the big bang and ending at the Big Chill. Show as many important events as you can.
To measure the parallax of a star, its angle on the sky is measured twice, 6 months apart. The parallax angle is the difference between these two angles.
The resolution of a 10 cm telescope is 1 arcsecond. Increasing the size of the telescope doesn't increase the resolution because air turbulence distorts the image.
If a star has a parallax angle of 1 arcsecond, how far away is it in light years?
Define "noon" to be the instant when the sun is highest in the sky for a given day.
The summer solstice is the day of the year when the sun is highest in the sky.
Suppose a 10 meter vertical pole is planted on Wall Street, New York City. At noon on the summer solstice, what is the length of the shadow?
Suppose there are two synchronized clocks, one in New York City and another directly to the east in Brooklyn, and suppose you use these clocks to measure the time of sunset.
Sunset for the clock in New York City = 6:00 PM Sunset for the clock in Brooklyn = 5:57 PM
What is the distance between the clocks?
For each property there is a "Goldilocks zone" that is ideal for habitability. What are the consequences of if there is too much or too little of each property?
Why did Venus and Mars become uninhabitable?
A "*" indicates a link to a solution.
What is the minimum mass for a planet to have an atmosphere? Assume a temperature of 300 Kelvin. What is the minimum mass for a gas giant? *
The characteristic diffraction angle for a circular aperture is:
Wavelength = λ Aperture diameter = D Diffraction angle = θ = 1.22 λ / DWhat is the wavelength of green light with a wavelength of 555 nm?
What is the diameter of a pupil at maximum dilation?
What is the diffraction angle?
Conduct an experiment and determine the minimum angle for which you can resolve two dots.
For 20/20 vision, what is the angle of the smallest letter you can resolve?
Neptune is at the edge of detectability by the the human eye. How bright is Neptune in Watts/meter^{2} and how many photons/second does this correspond to?
How far can a 9 mm diameter lead bullet travel underwater before losing half its speed? Estimate the mass of the bullet and the recoil momentum of gun. How far does a soccer ball travel in air before losing half its speed? *
What is the maximum speed of a car with a 400 horsepower engine?
How far can a car go on 50 liters of gasoline at 75 mph?
If you detonate the bomb at the center and if the asteroid is too large, gravity will bring the asteroid back together. For a uniformdensity sphere,
Gravitational energy = .6 G Mass^{2} / RSuppose a hydrogen bomb has the energy of 10 megatons of TNT, which is 4*10^{16} Joules. What would you estimate is the largest value for the radius of an asteroid that this bomb can shatter?
In "Star Wars", a Death Star shatters a planet. If the planet is identical to the Earth, how much energy does this take? If the energy were provided by a sphere of antimatter with the density of iron, what is the radius of this sphere?
For a typical metal, estimate the value of the tensile modulus divided by the density.
Estimate the stopping distance of a cosmic ray proton in iron in units of tons/meter^{2}. *
Estimate the critical mass of Uranium235.
Estimate the minimum and maximum frequency of a string on a violin?
How does the minimum and maximum frequency scale with string length?
*
How far can a car go at 30 mph if it is powered by 100 kg of supercapacitors? *
What is the minimum power/weight ratio required for humanpowered flight? *
If a speaker with diameter D plays a note of frequency F, what is the maximum sound power that it can produce? *
For a passenger aircraft such as a 747 the maximum useful speed is just less than the speed of sound. If you go faster than this then the plane is less fuel efficient. What is the maximum thrust/meter^{2} of a jet engine moving at the speed of sound?
The SR71 uses ramjet engines. Estimate its maximum speed.
Estimate the maximum acceleration of an ion drive powered by Strontium90. Assume that the mass of the ion drive is less than the Strontium90 required to power it. (For the ChangDiaz ion drive they are approximately equal).
Estimate the maximum height of a tree.
The moon is spiraling outward and in the distant future it will be stolen by the sun. Estimate the maximum stable orbit radius for the moon. * *
If a planet is close enough to a star it becomes tidally locked to the star. Mercury is just barely close enough for this and it orbits such that
3 * Orbit period = 2 * Spin period
If it were any closer it would be forced into a lock such that
Orbit period = Spin period
All of the solar system's moons are locked to their planets in this way. None of the planets are locked to their moons except Pluto.
For a lowmass star, the habitable zone is closer to the star than it is for the sun. If the star is sufficiently small, a planet in the habitable zone will be close enough to be locked to the star and will experience extreme weather.
The luminosity of a star scales as mass to the 3.5 power.
Let L = Luminosity of a star / Luminosity of the sun (Watts).
If a star is such that the habitable zone is at Mercury's orbit, what is L? What stellar mass corresponds to this luminosity?
Atomic cooling experiments can reach temperatures of ~ 10^{7} Kelvin. For this temperature, what is the quantummechanical wavelength of a rubidium atom?
Using Wikipedia, what is the mass, luminosity (Energy/time), and lifetime of the sun? What is the distance from the Sun to the Earth and what is the radius of the Earth?
How many kilograms of sunlight fall on the Earth each second?
If we assume that the sun's luminosity throughout its lifetime is equal to its present luminosity, how much energy does it produce in its lifetime? How many Earth masses is this? What fraction of the sun's mass is this?
For a proton ring collider, what is the proton energy as a function of ring radius, assuming a ringaveraged magnet strength of 10 Tesla. *
For an electron ring collider, the maximum energy is limited by synchrotron radiation. What is the maximum energy as a function of radius? *
The maximum energy of an electron linear collider is limited by synchrotron radiation from the curvature of the Earth. What is the maximum energy? *
For a muon in a ring collider, how many times does the muon go around the ring during one halflife? *
Cosmic rays crashing into the atmosphere produce muons, many of which reach the surface. Using data from Wikipedia, what is the typical altitude of muon production? What is the halflife of a muon and how far does it travel during this time if it is moving at close to the speed of light?
What is the lowestenergy cosmic ray that can reach Earth's orbit?
What is the furthest distance we could detect an Earthlike planet in the Kuiper belt? *
Construct a method for deflecting an asteroid and estimate the maximumsized asteroid it can deflect, if we have 1 year of advance warning. *
A = Area of a room H = Height of a room N = People in a room D = Surface density of people in the room = D/A C = Carbon dioxide fraction in the air dC = Change in carbon dioxide fraction per second Cmax= Maximum save carbon dioxide fraction in the air Ct = Time for the carbon dioxide fraction to go from 0 to Cmax T = Temperature in the room dT = Change in room temperature per second Tmax= Maximum tolerable change in room temperature = 5 Kelvin Tt = Time for the temperature to increase by Tmax W = Water vapor fraction in the air dW = Change in water vapor fraction per second Wmax= Saturation vapor pressure of water at 293 Kelvin Wt = Time for the water vapor fraction to go from 0 to Wmax P = Power generated per person = 100 WattsWhat is Ct, Wt, and Tt?
For each planet, what is the largest moon?
What is the name of the largest asteroid?
Name as many other asteroids as you can.
What is the name of the telescope we use to find asteroids with?
What is the name of the new telescope that will succeed it?
What are the names of the 2 small galaxies near the Milky Way?
When Uranus was first discovered by Herschel, what name did he give it?
What is the theme for the names of the moons of Uranus?
What is the name of the largest radio telescope?
What is the name of the telescope that will succeed the Hubble? Where will it be located?
The data that Kepler used to prove that planets orbit as ellipses was taken by whom?
What kind of light is the Webb telescope optimized for?
The measurements that Aristarchus did were improved upon by what Indian mathematician?
What is the name of the telescope that finds planets by eclipse?
What are the names of the 5 moons of Pluto?
Name as many Kuiper belt objects as you can
Among all known Kuiper belt objects, which is furthest from the sun?
Where is the Oort cloud?
Who invented the pendulum clock?
On the flags of Australia and New Zealand, what is the name of the constellation depicted?
What is the Messier Catalog number for the Andromeda galaxy?
Name as many galaxy superclusters as you can.
What is the speed of the Earth's orbit around the sun?
How far away is the center of the galaxy?
How fast is the sun moving in its orbit around the center of the Milky Way?
How fast is the Milky Way moving with respect to the cosmic microwave background?
What is the orbital velocity for the Earth?
What is the escape velocity from the surface?
Of the five Lagrange points, which are stable?
Other than the Milky Way and Andromeda, name as many galaxies as you can.
Other than the sun and the stars in the Alpha Centauri system, name as many stars as you can.
In units of solar masses, what is the minimum mass to be a star?
For rocket engines, what is the most powerful possible chemical reaction?
Name as many noble gases as you can.
What elements are liquids at room temperature?
Gold was an uncounterfeitable currency until the discovery of what element?
Which three elements are the active ingredient in fertilizer?
Name the elements that are more dense than gold.
What is the densest element?
What is the most abundant element in the Earth's crust?
What is the most abundant element in a metallic meteorite?
What is the element to the right of iron?
What is the element below chromium?
What is the element below oxygen?
What is the element to the right of carbon?
What is the element with the lowest proton number that has no stable isotopes?
Name as many metals as you can that have a proton number that is less than that for iron.
Name as many metals as you can that have a proton number that is greater than that for iron.
In the 16th century, who brought decimal numbers to Europe?
In what century were cannons first used?
Before the discovery of iron, what metal was used for swords?
Who discovered that electric currents attract?
Other than Neil Armstrong, name as many astronauts as you can that have been on the moon.
Who discovered that an electric current attracts a compass?
In what year did humans first walk on the moon?
What is the most recent year that humans walked on the moon?
At the Large Hadron Collider, what particle was recently discovered?
In units of Celsius, what is the temperature of absolute zero?
How many different DNA codons are possible?
What is the order of atoms in a protein backbone?
What would you estimate is the mass of a 16 inch diameter pizza with sausage, Canadian bacon, Parmesan cheese, olives, mushrooms, onions, and peppers? What is an estimate of the mass of each ingredient?
What is the speed of the sun's orbit around the center of the galaxy and what is its distance from the center of the galaxy? Using this, what is the mass of material interior to the sun?
How many stars are there interior to the sun, what is their average mass, and what is the total mass of stars interior to the sun?
Cannon mass * Cannon recoil velocity =  Cannonball mass * Cannonball velocity 2000 * Cannon recoil velocity =  10 * 600 Cannon recoil velocity = 3 meters/second
Initial vertical velocity = Acceleration * Time to reach the top of the arc 30 = 10 * Time to reach the top of the arc Time to reach the top of the arc = 3 secondsThe football travels upward for 3 seconds and downward for 3 seconds before hitting the ground. The total hang time is 6 seconds.
Horizontal distance traveled = Horizontal velocity * Hang time = 20 * 6 = 120 meters
Total force = Jet force + Gravity force = 1800 + Mass * Gravityconstant = 1800  110 * 10 = 600 Acceleration = Total force / Mass = 600 / 110 = 5 m/s^{2} (upward)
Acceleration = Velocity / Time = 20 / 5 = 4 m/s^{2} Distance = .5 * Acceleration * Time^{2} = .5 * 4 * 5^{2} = 50 meters
Energy = Mass * g * Height = 110 * 10 * 12 = 13200 Joules Power = 13200 / 5 = 2640 Watts
Centripetal force = Maximum friction force Mass V^{2} / R = FrictionCoefficient * Mass * g V = Squareroot(Frictioncoefficient * g *R) = Squareroot(.9 * 10 * 8) = 8.5
Mass = Density * Volume = 19.3 * 3^{3} = 521.1 grams Price = Price/gram * Grams = 40 * 521.1 = 20800 $Speed of a baseball pitch thrown by Randy Johnson 45 meters/second Initial height of the baseball 2.2 meters Distance from the pitcher to the batter 20 meters
Time to travel from pitcher to catcher = Distance / Velocity = 20 / 45 = .44 seconds Vertical drop = .5 * Acceleration * Time^{2} = .5 * 10 * .44^{2} = .99 meters
Maximum acceleration = Maximum friction force / Mass = Friction coefficient * Downforce / Mass = Friction coefficient * Mass * g / Mass = 1.4 * 10 = 14
G = Gravity constant M = Mass of Earth R = Radius of Earth A = Gravitational acceleration at the surface of the Earth = G M / R^{2} = 6.67e11 * 5.97e24 / 6372000**2 = 9.8 m/s^{2} A = Gravitational acceleration at an altitude of 400 km = G M / R^{2} = 6.67e11 * 5.97e24 / (6372000+400000)^{2} = 8.7 m/s^{2} Gravitational energy = Mass * g * Height = 1 * 10 * 400000 = 4e6 Kinetic energy = .5 * Mass * Velocity^{2} = .5 * 1 * 7800000^{2} = 3e13
Distance between two train tracks = 1.435 meters Central Park length = 4.0 km Central Park width = .8 km Traffic light diameter =20.3 cm Stop sign size = 75 cm Distance between opposite edges Stop sign letter height = 25 cm Height of Tyrion Lannister = 135 cm 4 feet 5 inches Standard sheet of paper, height =27.9 cm 11 inches Standard sheet of paper, width =21.6 cm 8.5 inches Manhattan island length =21.6 km Distance between Manhattan streets= 78 meters = Central park length / Central park streets = 4.0 km / (110  59)
For an electron that is 10^{15} meters from another electron, what is the force?
F_{ele} = Electric force between two protons separated by 1 meter F_{grav} = Gravity frce between two protons separated by 1 meter Q = F_{ele} / _{grav}What is Q?
Volume of the drink = V Fraction of alcohol = F Volume of alcohol = A = F V Volume of alcohol in Bonds = B = A / .5 ounces Beer: F V = .05 * 12 = ounces (One "Bond") One ounce = 29.57 mL One gallon = 128 ounces In ounces: F V A B Beer .05 12 .6 1 Wine glass .13 4.6 .6 1 Scotch shot .40 1.5 .6 1 Wine bottle .13 25.4 3.3 5.5 Scotch bottle .40 25.4 10.1 16.9 Keg .05 1984 99.2 165.3
Gold has a density of 19.3 g/cm^{3}. What is the mass of a gold cube that is 3 cm on a side?
Gold costs 40 $/gram. What is the price of the gold cube?
What is the mass of CO2 in the Earth's atmosphere and how many Pinatubos would it take to double the atmosphere's CO2?
What is the mass of the Earth's atmosphere, what is the mass of the carbon dioxide it contains, and what is the mass of elemental carbon contained in the carbon dioxide?
Wavelength * Frequency = WavespeedThe wavelength of visible light is 5.55e7 meters. What is the frequency?
A violin Astring has a frequency of 440 Hertz and the speed of sound is 340 m/s. What is the wavelength of this wave?
For a computer screen 20 cm from your eyes, what is the minimum size of letters you can see?
If each letter is 7 pixels then how many pixels does a 10 cm screen have? (This is a "retinal" display)
A ten centimeter telescope is 20 times more powerful that a human with 20/20 vision. If giant letters are painted on the moon, what is the minimum size of letters that the telescope can see?
How many kg of water flow through the Mississippi per year, and how many people can it feed if it is used to grow rice?
Energy = Mass * Speedoflight^{2}How much mass does this energy correspond to?
C_{8}H_{18} + 25 O_{2} > 9 H_{2}O + 8 CO_{2} M_{octane} = Mass of octane in the reaction M_{oxygen} = Mass of oxygen in the reactionWhat is M_{oxygen}/M_{octane}?
R = Radius of an asteroid P = Probability per millenium of a hit from an asteroid at least as large as RUsing data from the web, what is P for R = .01, .1, 1, 10 km?
What would you estimate is the mass of a 16 inch diameter pizza with sausage, Canadian bacon, Parmesan cheese, olives, mushrooms, onions, and peppers? What is an estimate of the mass of each ingredient?
Kinetic energy = ½ Mass Velocity^{2}If a rocket nozzle converts this energy into kinetic energy of exhaust, how fast is the exhaust moving?
If a solar cell produces 1000 Watts, estimate how long it takes to produce enough energy to convert 1 ton of water to hydrogen and oxygen gas?
How are the PanSTARRS and LSST telescopes different from conventional telescopes like Keck? What can they do that Keck can't?
Force required to break the wire = F (Newtons) Crosssectional area of the wire = A (meters^{2}) Tensile strength of the wire = S = 2⋅10^{8 Newtons/meter2 }If a person with a weight of 1000 Newtons (100 kg) hangs from this wire, what is the minimum crosssectional area for the wire to not break? What is the diameter of this wire?
Without using the web, estimate: (show how you arrived at each estimation)
The number of students at the University of Wisconsin.
The number of bars on State Street (half of the bars are located here).
The amount of beer consumed per week in pints and kegs.
The number of 18wheel trucks required to carry the kegs.
Without using the web, estimate the number of 20 dollar bills that a typical briefcase can carry. If the bills are replaced with gold, how many $ worth of gold is this? (Assume gold costs 35000 $/kg).
Your brain contains 10^{13} bytes of information. If this information is stored on micro SD cards, how many suitcases would it take to carry them?
Time = T seconds Solar cell efficiency = C = .25 dimensionless Area of a solar cell = A meters^{2} Average solar intensity in Arizona = S_{sol} = 250 Watts/meter^{2} (Averaged over day and night) Power generated by a solar cell = P = C A S_{sol} Energy generated by a solar cell = E = P T Joules United States population = N = 318 million United States electricity per person = P_{cap} = 1700 Watts United states electrical power = P_{USA} = N P_{cap} = 4.5⋅10^{11} WattsWhat is "A", the area of solar cells required to provide America's electricity?
Lead volume = S_{lead} (meters^{3}) Gunpowder volume = S_{powder} (meters^{3}) Lead density = D_{lead} = 11400 kg/meters^{3} Gunpowder density = D_{powder} = 1400 kg/meters^{3} Lead mass = M_{lead} = D_{lead} S_{lead} Gunpowder mass = M_{powder} = D_{powder} S_{powder} Gunpowder energy density = Q_{powder} = 5.2⋅10^{6} Joules/meter^{3} Gunpowder energy = E_{powder} = Q_{powder} S_{powder} Lead velocity = V Lead kinetic energy = E_{lead} = ½ M_{lead} V^{2}If we assume that the lead and gunpowder volumes are equal and that all of the gunpowder energy goes into lead kinetic energy, what is the speed V of the lead?
Mass = M Gravity constant = g = 10 m/s^{2} Height = H Gravity energy = E_{g} = M g H Human sprint speed = V = 10 m/s Kinetic energy = E_{k} = ½ M V^{2}In a pole vault, kinetic energy is converted to gravitational energy. We can approximate how high the vaulter goes by setting E_{k}=E_{g}. Given this assumption, what is H?
Using Wikipedia, what is the number of neurons in the brain?
What is the speed of sound and how long does it take sound to go all the way around the Earth?
What is the momentum of 1 Joule of light?
What is the momentum of a golf ball with 1 Joule of kinetic energy?
If a photon collides headon with an electron, the electron is set in motion and the photon recoils backwards with a reduced frequency. In this experiment the observables are:
F = Frequency of photon before collision This photon is traveling to the right at speed C. Frequency is measured in Hertz or cycles per second f = Frequency of photon after collision This photon is traveling to the left at speed C. V = Velocity of the electron after the collision This electron is moving to the right at speed C. Before the collision, the electron is at rest. M = Mass of an electron = 9.109*e31 kgWe assume that the photon has a low enough frequency so that the recoiling electron is not relativistic. This applies if the photon is less energetic than an Xray. In this case,
V << C (Ff)/F << 1 The change in frequency is small compared to the initial frequencyIf you do the experiment and measure the observables you find that (in MKS units)
F  f = 1.62e20 * F^{2} Hertz V = 4.85e12 * F meters/secondGiven this result, how would you construct formulas for the energy and momentum of a photon?
E = Energy of the initial photon Q = Momentum of the initial photonThe photon frequency is almost the same before and after the collision, and so we assume that the change in photon momentum during the collision is 2Q. This momentum is taken up by the electron.
2 Q = M V Q = M V / 2 = 2.21e42 F Electron energy = hF  hf = h(Ff)We can express the photon momentum in terms of the Planck constant.
Q = 2.21e42 F = h F / 3e8 (3e8 happens to be the speed of light) = h F / CHence the photon energy and momentum are
F = Photon frequency W = Photon wavelength C = Speed of light = F W E = Photon energy = h F Q = Photon momentum = h F / C = h / WThe momentum and wavelength are related by
Q W = h E = Photon energy = h F Q = Photon momentum = h F / C = h / WThe momentum and wavelength are related by
Q W = hThis is the "de Broglie" relation, and it is true both for photons and for particles with mass. Every particle with mass has an associated wavelength W which is its quantummechanical "size".
Photons and electrons have a different relationship between energy and momentum.
For a photon, Energy = Momentum * C For an electron, Energy = Momentum^{2} / (2*Mass)
Volume of the drink = V Fraction of alcohol = F Volume of alcohol = A = F V Volume of alcohol in Bonds = B = A / .5 ounces Beer: F V = .05 * 12 = ounces (One "Bond") One ounce = 29.57 mL One gallon = 128 ounces In ounces: F V A B Beer .05 12 .6 1 Wine glass .13 4.6 .6 1 Scotch shot .40 1.5 .6 1 Wine bottle .13 25.4 3.3 5.5 Scotch bottle .40 25.4 10.1 16.9 Keg .05 1984 99.2 165.3