HP, short for horsepower, can be defined as the amount of work completed in a unit or specified amount of time. By simply comparing the volumes between the tetrahedron and octahedron when they collide, we get the fine structure constant. He concluded that, compared to the cost of moving bytes around, everything else is free. From this Mg information, we have T5 = 2T2, soT2 =. 2 Then T1 = T2 = T3 = Mg 3 Mg, and T4 =, and 2 2 T5 = Mg. (b) Since F = T1, we have F = Mg. 2 FIG.

In this project, you can do a similar experiment without having to worry about falling from a circus tightrope. Move the weight or piece of clay to some new place on the stick. There is no way whatsoever to measure the distance between A and B because there is nothing to compare the positions of the balls to. Therefore, to the extent that a planet can be considered to be made up of a series of concentric shells, where each shell has a uniform density, then equation 9 applies directly and simply.

Surround it with a close-fitting gaussian surface. At around this time (1907), he also started to wonder how Newtonian gravitation would have to be modified to fit in with special relativity, and how the effects of gravity could be incorporated into the formulation. Whatever one might think about string theory's relationship with anthropic reasoning, we do have here a potential explanation of a previously inexplicable piece of old empirical data, which ought to lend some credence to the theory.

So the collapse speed was less than half of free-fall speed. Newton’s law had a flaw: It did not explain how one thing could act on another instantly, across any distance, with nothing in between. P10.23 In the rod along the x-axis, the bit of material between x and x + dx has mass distance r = x 2 + FG L IJ H 2K FG m IJ dx and is at H LK 2 from the axis of rotation. The woman smiled at Einstein and replied, "Si." Please try logging in or sending yourself a password reminder.

Thus, 2 Substitute (1) into (2) to obtain: R2 =. 1 1 = = 84.7 s slope 0.011 8 τ 84.7 s = 8.47 µF. Suppose that, at the ambient temperature, sound moves at 340 m/s; and suppose that the horizontal width of each row of seats is 60 cm. P9.55 fk = −235 N i (c) For the person, pi + I = p f mvi + Ft = mv f b60.0 kg g4.00 m s − a235 Nft = b60.0 kg g1.33 m s t = 0.680 s a f person: mv f − mv i = 60.0 kg 1.33 − 4.00 m s = −160 N ⋅ si cart: (d) 120 kg 1.33 m s − 0 = +160 N ⋅ si b g a f (e) x f − xi = 1 1 4.00 + 1.33 m s 0.680 s = 1.81 m vi + v f t = 2 2 (f) x f − xi = 1 1 vi + v f t = 0 + 1.33 m s 0.680 s = 0.454 m 2 2 (g) 1 1 1 mv 2 − mvi2 = 60.0 kg 1.33 m s f 2 2 2 (h) 1 1 1 mv 2 − mvi2 = 120.0 kg 1.33 m s f 2 2 2 (i) d d i b i g b b g 2 − g 2 b 1 60.0 kg 4.00 m s 2 g 2 = −427 J − 0 = 107 J The force exerted by the person on the cart must equal in magnitude and opposite in direction to the force exerted by the cart on the person.

P37.70 λ 6 2 Lλ λ 2 + L2 + d 2 = L2 + 6 36 L2 + d 2 − L = The last term is negligible d= P37.71 FG 2Lλ IJ H6K 12 = a f 2 1. 2 m 620 × 10 −9 m = 0.498 mm. 6 Superposing the two vectors, ER = E1 + E 2 ER = E 1 + E 2 = ER = FG E H 0 + E0 cos φ 3 IJ + FG E sin φIJ K H3 K 2 0 2 2 = E0 + E2 E2 2 2 E0 cos φ + 0 cos 2 φ + 0 sin 2 φ 3 9 9 10 2 2 2 E0 + E0 cos φ 9 3 Since intensity is proportional to the square of the amplitude, I= 10 2 I max + I max cos φ. 9 3 Using the trigonometric identity cos φ = 2 cos 2 I= or FG H IJ K φ − 1, this becomes 2 φ φ 10 2 4 4 I max + I max 2 cos 2 − 1 = I max + I max cos 2, 9 3 2 9 3 2 I= FG H φ 4 I max 1 + 3 cos 2 9 2 IJ K. φ E 406 Interference of Light Waves ANSWERS TO EVEN PROBLEMS P37.2 515 nm P37.40 1.20 mm P37.4 (a) 36.2°; (b) 5.08 cm; (c) 508 THz P37.42 449 nm; blue P37.6 maxima at 0°, 29.1°, 76.3°; minima at 14.1° and 46.8° P37.44 (a) see the solution; (b) 2.74 m P37.8 36.2 cm P37.46 P37.10 641 number of antinodes = number of constructive interference zones = 1 plus 2 times the greatest positive d integer ≤ P37.12 6.33 mm s P37.14 see the solution P37.16 (a) 1.29 rad; (b) 99.8 nm P37.18 0.968 P37.20 (a) see the solution; (b) 9.00 P37.22 (a) 2.88E0 at 0.349 rad; P37.24 P37.26 FG H IJ K P37.48 (b) 2.00E0 at (d) E0 at λ number of nodes = number of destructive interference zones = 2 times the greatest d 1 positive integer < + λ 2 3π rad 2 see the solution FG H IJ K 1 λ where 48 m = 0, 1, 2, 3, … x1 − x 2 = m − P37.28 see the solution P37.30 612 nm P37.32 512 nm P37.34 96.2 nm P37.36 (a) 238 nm; (b) λ increase; (c) 328 nm P37.38 1.31 P37.50 5.00 km 2 P37.52 2.50 mm P37.54 113 P37.56 π rad; (c) 0; 3 λ 2 n −1 115 nm P37.58 (a) see the solution; (b) 266 nm P37.60 see the solution P37.62 see the solution P37.64 (a) 14.7 µm; (b) 1.53 cm; (c) −16.0 m P37.66 7.99 sin ω t + 4.44 rad P37.68 130 nm P37.70 0.498 mm a f b g 38 Diffraction Patterns and Polarization CHAPTER OUTLINE 38.1 38.2 38.3 38.4 38.5 38.6 Introduction to Diffraction Patterns Diffraction Patterns from Narrow Slits Resolution of Single-Slit and Circular Apertures The Diffraction Grating Diffraction of X-Rays by Crystals Polarization of Light Waves ANSWERS TO QUESTIONS Q38.1 Audible sound has wavelengths on the order of meters or centimeters, while visible light has a wavelength on the order of half a micrometer.

The sequence of events—and thus time—goes in only one direction. U0 2 = e j κC 0 ∆V02 2 The extra energy comes from (part of the) electrical work done by the battery in separating the extra charge. (b) Q 0 = C 0 ∆V0 and so Q = C∆V0 = κC 0 ∆V0 Q =κ. The black hole apparently doesn't “remember” what falls in: Electrons, iron atoms, dark matter, and even photons can all contribute to its mass. It was found that the orbit period is declining: the two astronomical bodies are rotating faster and faster about each other in an increasingly tight orbit.

Indeed, it is a major challenge of loop quantum gravity to show that it indeed has general relativity as a low-energy limit, and a major challenge of string theory to show that it has the standard model of particle physics plus general relativity as a low-energy limit. Here's a metaphor I constructed: Imagine you are a tribesman from the Amazon rainforest and you have no experience of the world at large; one day you stumble upon C21st civilization in the form of a man with a remote control airplane.

He said there would be more information coming, but I never heard about it again. You might imagine that it's the distance to the surface of the earth, that's how high up the satellite is. Nevertheless, scientists expect that a force-transmitting particle - the graviton - exists. The field’s direction is (c) Consider a strip of the wall of width dx and length. An object of mass m at the earth's surface is Re from the earth's centre.

The potential energy when the car is at point B is given by U B = mgy where y is the vertical distance of point B below point A. Gravity is the amount of force that pulls toward an object. The passengers would feel as if they are experiencing a force. The plans are well illustrated, and supplies are easy to find in most hardware stores and on the internet. Perhaps about half as often, it is 4 × 1.6 min. These highly nonlinear equations feature N arbitrary coupling constants, yet they can be solved by algebraic operations and if all the N coupling constants are real and rational the corresponding N-body problem is isochronous: its generic solutions are all completely periodic with an overall period T independent of the initial data (but many solutions feature subperiods T/p with p integer).