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Review Chapters 9-14 Classical Relativity A Reference System Reference system : the set of objects that are not moving relative to each other and that can be therefore used as the basis for detecting and describing motion. Galileo asked if observers could decide whose description was “correct”. He concluded that they couldn’t. In fact, each observer’s description was correct! Galilean Principle of Relativity The laws of physics are the same for all inertial reference systems. Questions 1. Alice in Wonderland begins with Alice falling down a deep, deep rabbit hole. As she falls, she notices that the hole is lined with shelves and grabs a jar of orange marmalade. She is afraid to drop the jar for it might hit somebody on the head. What would really happen to the jar if Alice had dropped it? Describe its motion from Alice’s reference system and from the reference system of someone sitting on the shelf. You wake up in a windowless room on a train, which rides along particularly smooth tracks. Imagine that you have a collection of objects and measuring devices in your room. What experiment could you do to determine whether the train is stopped at the train station or moving horizontally at a constant velocity? Assume that you are riding in a windowless train on perfectly smooth tracks. Imagine that you have a collection of objects and measuring devices in the train. What experiment could you do to determine whether the train is moving horizontally at a constant velocity or is speeding up? Accelerating Reference System Forces that arise in accelerating reference systems are called inertial forces. Another common label for these forces is fictitious forces. Special Theory of Relativity Postulates of the Special Theory of Relativity The idea of an absolute frame of reference was gone with the idea of stationary ether. First Postulate All laws of nature are the same in all uniformly moving frames of reference. Second Postulate The speed of light in the free space has the same measured value for all observers, regardless of the motion of the source or the motion of the observer; that is, the speed of light is a constant. Simultaneity Two events that are simultaneous in one frame of reference need not be simultaneous in a frame of reference moving relative to the first frame. This non simultaneity of events in one frame that are simultaneous in another is a purely relativistic effect – a consequence of light always having the same speed for all observers. Two side-by side observers at rest relative to each other share the same reference frame. Both would agree on measurements of space and time intervals between given events, so we say they share the same realm of spacetime. Time Dilation Lorentz Factor, g g 1 v 1 2 c 2 If you are moving in a spaceship at a high speed relative to the Earth, would you notice a difference in your pulse rate? In the pulse rate of people back on the Earth? Will observers A and B agree on measurements of time if A moves at half the speed of light relative to B? If both A and B move together at half the speed of light relative to the Earth? Space travelers on the way to colonize a planet orbiting a distant star decide to cook a “three-minute-egg”. Would a clock on Earth record the cooking time as less than, equal to or greater than 3 minutes? Why? In an experiment to measure the lifetime of muons moving through the laboratory, scientists obtained an average value of 8 microseconds before a muon decayed into an electron and two neutrinos. If the muons were at rest in the laboratory, would they have a longer, a shorter, or the same average life? Why? Length Contraction L L0 1 v / c 2 2 E mc 2 Peter volunteers to serve on the first mission to visit Alpha Centauri. Even traveling of 80% of the speed of light, the round-trip will take a minimum of 10 years. When Peter returns from the trip, how will his biological age compare with that of his twin brother Paul, who will remain on Earth? Is it physically possible for a 30-year-old college professor to be a natural parent of 40-year-old student? Is it possible for length contraction to occur without time dilation? Explain. Suppose the meter stick zips by you at a speed only slightly less than the speed of light. If you measure the length of the meter stick as it goes by, would you determine it to be longer than, shorter than, or equal to 1 meter long? Why? General Theory of Relativity The principle of equivalence states that observations made in an accelerated reference system are indistinguishable from observations made in a Newtonian gravitational field. An astronaut awakes in her closed capsule, which actually sits on the moon. Can she tell whether her weight is the result of gravitation or acceleration motion? Explain. You wake up at night in your berth on a train to find yourself “pulled” to one side of the train. You naturally assume that the train is rounding a curve but you are puzzled that you don’t hear any sounds of motion. Offer another possible explanation that involves only gravity, not acceleration in your frame of reference. Bending of Light by Gravity According to the principle of equivalence, if light is deflected by acceleration, it must be deflected by gravity. Gravity and Time According to Einstein’s general theory of relativity, gravitation causes time to slow down. The Atomic Hypothesis 1. The ideal gas model accounts very well for the behavior of gases at standard temperature and pressure. Would the ideal gas model begin to fail for very large pressures or for very small pressures? Explain your answer. 2. A cube and a spherical ball are made of the same material and have the same mass. Which exerts the larger pressure on the floor? 1. You may apply enough force to the head of a pushpin to push it into a plaster wall with you thumb. However, it is not a good idea to try to do this with a needle. Use the concept of pressure to explain the difference between these two situations. 2. If you screw the cup of empty plastic drinking bottle on tightly while walking in the mountains, why are the sides of the bottle caved in when you return to the valley? 1. Your right rear tire has to support a weight of 3000 N. Normally, the contact area of your tire with the road is 200 square cm. If the pressure in your tire is suddenly reduced from 32 pounds per square inch to 16 pounds per square inch, what must be the new contact area to support the car? 2. Use the microscopic model of gas to explain why the pressure in a tire increases as you add more air. 1. If the average speed of a perfume molecule is 500 meters per second, why does it take several minutes before you smell the perfume from a bottle opened across the room? 2. What happens to the average speed of the molecules of a gas as it is heated? States of Matter Vdisplaced V0 0 fluid The fraction of object submerged is given by the ration of the object’s density to that of the fluid. Pascal’s Principle A change in pressure at any point in an enclosed fluid at rest is transmitted undiminished to all points in the fluid. 1. What shape would you expect a drop of water to take if it were suspended in the air in the space shuttle? 2. If you fill a glass with water so the water is level with the top of the glass, you can carefully drop several pennies into the glass without spilling any water. How do you explain this? 3. Are you ears going to hurt more swimming 12 feet down in your swimming pool or 12 feet down in the middle of Lake Superior? Explain. 1. Fresh water has a density of 1000 kg per cubic meter at 4C and 998 kg per cubic meter at 20C. In which temperature water would you feel the greater pressure at the depth of 10 meters? Why? 2. Salt water is denser than fresh water. Would a scuba diver have to go deeper in salt water or in fresh water to reach the same pressure? Why? 3. Use Archimedes’ principle to explain why an empty freighter sits higher in the water than a loaded one. Barometers 1. Is there a buoyant force acting on you in the air? If there is, why you are not buoyed up with this force? 2. How does buoyancy change as heliumfilled balloon ascends? Bernoulli’s Principle Where the speed of a fluid increases, internal pressure in the fluid decreases. 1. A scuba diver achieves neutral buoyancy by adjusting the volume of air in her buoyancy compensator vest (BCD) so that the buoyant force equals her weight. If she then kicks her fins and swims down an additional 20 feet, will the net force now be upward, zero or downward? Explain. The Nature of Heat Zeroth Law of Thermodynamics If two systems are in thermal equilibrium with a third system, then they are in thermal equilibrium with each other. First Law of Thermodynamics The increase in internal energy of a system is equal to the heat added plus the work done on the system. Third Law of Thermodynamics Absolute zero ma be approached but experimentally but can never be reached. Specific Heat The amount of heat it takes to increase the temperature of an object by 10C is known as heat capacity of the object. Change of State Latent Heat If a material changes phase from solid to liquid, or from liquid to gas, a certain amount of energy is involved in its change of phase. 1. If you make the mistake of removing ice cubes from the freezer with wet hands, the ice cubes will stick to your hands. Why does the water on your hands freeze rather than the ice cube melt? 2. In northern climates drivers often encounter signs that read “BRIDGE FREEZES BEFORE ROADWAY”. Why does this occur?