6.1: Energy of all shapes and sizes A. What is Energy? (a) Watt (b) Joule (c) Erg 2 Why does an electric bill have W-hrs listed on it? 3 What is the speed of light in centimeter-gram-second units? 4 Organize the following by least to most energy: A. The merger of two black holes. B. A solar flare. C. A supernova. D. The dinosaur-killing meteor impact. B. Kinetic Energy (a) Bulk Motion (b) Thermal Motion (c) Momentum (d) Kinetic Energy [equation] 2 Which is a moon orbiting a planet: bulk or thermal?
3 Which of the following has the greatest kinetic energy? A. A 1 kg satellite moving at 4 m/s. B. A 1000 kg space station that is stationary. C. A 2 kg wrench moving through space at 3 m/s. 4 What speed would a 500 kg comet have to be traveling at to match the kinetic energy of a 10g asteroid moving at 700 m/s? (a) Set up the problem: 1 2 m 1v 2 1 = 1 2 m 2v 2 2 (b) Rearrange to find v 1 (c) Plug in the values from the problem! Make sure you convert the tiny asteroid to kilograms first. C. Potential Energy (a) Gravitational Potential (b) Nuclear Potential (c) Chemical Potential (d) Electromagnetic Potential 2 Why is gravitational potential energy negative? 3 What type of potential energy does rocket fuel have? What type does it overcome? 4 How much energy does it take for the Death Star to blow up Alderaan? (a) We need to find how much energy we need to inject in order to overcome the gravitational energy holding the planet together. (b) After some nifty calculus, we find that the gravitational energy is E g = 3 GM 2. 5 r (c) Alderaan has r A =6, 250 km and has a mass of m A =5.7 10 24 kg. Plug in the numbers! (d) The sun irradiates the Earth with 1370 W/m 2 of energy. Assuming we could make a collecting area of 10 6 m 2, how long would it take to gather this much energy? 5 What is the gravitational force of Jupiter on you right now, compared to the gravitational force I am exerting on you? (a) Write down a ratio equation for the relative force contributions: F 1 F 2 = GM 1 m r 2 1 GM 2 m r 2 2 Page 2
(b) Simplify the equation. (c) Let s say that I weigh m M =100kg, and am r M =10m away from you. Jupiter weighs m J =1.89 10 27 kg and has a closest approach of 4.4 10 11 m. Who exerts more force on you? D. Putting Energy together (a) Einstein s Energy Equation 2 Whiteboard Exercise: List sources of energy you are participating in right now. Bonus made order-of-magnitude guesses! E. Angular Momentum and Conservation of Energy (a) Angular Momentum (b) Centripetal Force 2 In the diagram below, which path will the ball take? 3 How does the binary relationship apply to the Earth-moon system? Page 3
(a) The moon and the earth both exert equal centripetal force on each other: m ev 2 e r e = m mv 2 m r m (b) BUT, v e = v m, as they are orbiting each other! Simplify the equation with this. (c) Where is the center of mass in the Earth-Moon system as a fraction of the Earth radius (R e =6.38 10 6 )? 4 True or False: You can point at an object in space and head toward it, as George Clooney and Sandra Bullock do more or less throughout all of Gravity. 5 What is the ideal radius for a communications satellite that we want to point at one location on the Earth always? (a) First, relate the kinetic energy equation to the gravitational potential energy equation: 1 2 mv2 = GMm r (b) Identify the variables in particular, how is r defined? (c) If the period (length of time) to travel around the circumference of a circle is given by T = 2fir, rearrange the equation to solve for the velocity. In order to point at v one location on Earth, we want a period equal to 24 hours, or 86,400 seconds. (d) Substitute the velocity you found into the relationship from the first part of the question. (e) Plug in the numbers and calculate the distance from the Earth s center! (f) If Earth s radius is r e =6.38 10 6 m, how far above the surface is the orbit? 6 Which is the most energy ine cient thing New Horizons could have done? A. Run on interplanetary cruise. B. Use Jupiter as a gravitational slingshot. C. Apply the brakes. D. Use the scientific instruments. Page 4
6.2: Gravity, Space, and Light A. Gravity (a) Equivalence Principle (b) Graviton (c) Quantum Gravity 2 In 1971, Alan Shepard hit two drives on the lunar surface. The golf ball traveled 2.5 miles in a 70 second hangtime. Why did the golf ball travel so far? 3 What does the magnet-earth experiment about the relative strength of the electromagnetic and gravitational forces? B. How Space A ects Light (a) Doppler Shift (b) Rest Frequency (c) Redshift (d) Blueshift 2 If our rest wavelength is green, what color would someone moving away (redshift) observe? How about a blueshift (moving toward us)? 3 The top is the spectra in lab; the bottom is the spectra of a moving object. Is it moving toward or away from us? 4 Two identical stars are observed from the Earth. Star A s emission lines (that are visible wavelengths in the rest frame) are observed to be at ultraviolet wavelengths. The same emission lines for Star B are observed to be at X-ray wavelengths. From these observations, what can you conclude? A. Both stars are moving away from the Earth. B. Star A is moving towards the Earth faster than Star B. C. Star B is moving towards the Earth faster than Star A. D. Star B is moving away from the Earth while Star A is moving towards the Earth. Page 5
C. Spacetime and Black Holes (a) Spacetime (b) Black Holes (c) Hawking Radiation (d) Gravitational Lens 2 Let s derive the event horizon, the radius from which no light can escape. (a) Relate the kinetic energy of a particle falling into the black hole to the gravitational potential energy. (b) How would this equation apply to light (hint: what is the velocity?) (c) r is called the Schwarzshild Radius. Rearrange the equation to find it. 3 If the Sun suddenly became a black hole, what would happen? 4 If we cannot see black holes, how do we know that they exist? 5 Do warp drives violate physics? Why or why not? Page 6