a) What is the measure of the area of the sofa according to Bob? b) What is the length of Bob’s Bike as measured by Alice? c) How long is the movie according to Bob? (the window is really wide!!!)
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Alice is sitting on her rectangular shaped sofa with dimensions of 2m × 1m (ignore the
other dimension), watching a movie that is 2 hours long. Bob is passing by Alice’s
window on his bike ( 2 m long) with a speed of 0.5c. If the length of the sofa is parallel to
the window,
a) What is the measure of the area of the sofa according to Bob?
b) What is the length of Bob’s Bike as measured by Alice?
c) How long is the movie according to Bob? (the window is really wide!!!)
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- A proton in the large hadron collider (LHC) travels at a relativistic velocity of 0.99c. mp = 1.67 x 10-27 kg. (a) What is the total energy in J, and eV (1.60 x 10-19 J/eV)? (b) What is the momentum? (c) What is the kinetic energyAs observed on earth, a certain type of bacteria is known to double in number every 24 hours. Two cultures of these bacteria are prepared, each consisting initially of one bacterium. One culture is left on earth and the other placed on a rocket that travels at a speed of 0.996c relative to the earth. At a time when the earthbound culture has grown to 64 bacteria, how many bacteria are in the culture on the rocket, according to an earth-based observer? Number i UnitsNeeds Complete typed solution with 100 % accuracy.
- Each measurement we take has a level of uncertainty in it. The smaller the uncertainty, the larger the precision our measurement has. Let's revisit how one might go about estimating the uncertainty in a measurement. If we assume our instrument is properly calibrated and we are not introducing systematic error through improper techniques, then if we take enough measurements, the average of these measurements will be around the true value. The upper and lower bounds of these measurements would then give us one method for determining our measuring device's uncertainty. (This of course is only true for a large set of measurements, but the approximation is good enough for now to get us started). For example, say we perform last week's experiment of pulling a block at a constant velocity with a force sensor across another rough surface. We take the following five measurements: F, = {2.51 N, 2.53 N, 2.50 N, 2.54 N, 2.49 N} The average of this dataset is F, = 2.51 N Now we have the choice of…Albert Einstein is pondering how to write his (soonto-be-famous) equation. He knows that energy E is a function of mass m and the speed of light c, but he doesn't know the functional relationship (E = m2c? E = mc4?). Pretend that Albert knows nothing about dimensional analysis, but since you are taking a fluid mechanics class, you help Albert come up with his equation. Use the step-by-step method of repeating variables to generate a dimensionless relationship between these parameters, showing all of your work. Compare this to Einstein's famous equation—does dimensional analysis give you the correct form of the equation?A cylindrical spaceship of length 35.0 m and diameter 8.35 m is traveling in the direction of its cylindrical axis (length). It passes by the Earth at a relative speed of 2.44××1088 m/s. a) What is the length of the ship, as measured by an Earth observer? b) What is the diameter of the ship, as measured by an Earth observer? c) How long does it take the spaceship to travel a distance of 10.0 km according to the ship's pilot? d) How long does it take the spaceship to travel a distance of 10.0 km according to an Earth-based observer?
- In special relativity, we introduced the momentum of a particle in a given Lorentz frame as p" = (E,p'), where E is the energy of the particle and p¹ is the relativistic 3-momentum. Explain why, in general relativity, the energy of a particle measured by an observer is given, irrespective of the coordinate system used, by -p Uobs, where p" is the momentum of the particle and uobs is the velocity of the observer in those coordinates.A particle has γ=18,399. a)Calculate c-v in m/s. (I would have asked for 1 - v/c, making the answer dimensionless, but the system doesn't seem to take numbers that small. Gamma is chosen to make the particle extremely close to the speed of light.) If your calculator gives problems, you might want to solve the appropriate equation for c-v or c(1 - v/c) and use an approximation. b) In the previous problem, in a race to the moon, by 3/4ths the distance, light is one or ten meters ahead of the particle. We routinely approximate mass as zero, gamma as infinite, and speed as the speed of light. ("Massless particles" -- gamma and m have to be eliminated from the expressions. Light is a true massless particle.) If a massless particle has momentum 1,739 MeV/c, calculate its energy in MeV.Uranium-238 decays via the alpha decay process. Part (a) Calculate the energy released in units of megaelectron volts when a uranium-238 nucleus undergoes alpha decay. Part (b) What fraction of the mass of a single uranium-238 nucleus is destroyed in the decay? Part (c) Why is difficult to observe the change in mass for a macroscopic sample of uranium-238?