For a colloidal sphere moving under the influence of Brownian motion in3D, what is the value of , and , the average velocities in each translational degrees of motion?
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- For mammals, resting heart rate scales as mass to the -1/4th power; that is, R is proportional to m^-1/4. The heart rate of a 5000 kg elephant is 30 bpm (beats per minute). What do you predict for the heart rate of a 5.0 kg monkey?For this problem, we want to estimate the answer, so our assumptions may be a little unrealistic. Suppose we want to estimate how much air we need to send to a space station, assuming we cannot recycle air. Suppose four astronauts are in a spherical space station. If each of them typically breathes about 500 cm³of air with each breathe, and take 15 breathes per minute (average resting value): a. What is the volume of air you would need in the space station if these four astronauts stayed for a full year? b. If the density of air is 1.25 kg/m³ and it costs (thanks to SpaceX) a mere $100/kg to send objects to the space station, how much money would the astronaut air supply cost?Vector B→B→ has magnitude 7.30 and direction 14.0° below the +x-axis. Vector C→C→ has x-component Cx = −2.00 and y-component Cy = −6.70. b. What is the y-component of B→B→ ? c. What is the magnitude of C→C→ ? d. What angle does C→C→ make with the +x-axis in counterclockwise direction? A positive angle is counterclockwise from the +x-axis. (answer in degreees) e. What is the magnitude of C→+B→C→+B→ ?
- The question is whether these relationships are linear or non-linear, can you please inform me on how I'd be able to tell?Under certain conditions, wind blowing past a rectangular speed limit sign can cause the sign to oscillate with a frequency w. (See the figure below and the Video.) Assume that w is a function of the sign width, b, sign height, h, wind velocity, V, air density, p, and an elastic constant, k, for the supporting pole. The constant, k, has dimensions of FL. Develop a suitable set of pi terms for this problem. SPEED LIMIT 40the average density of an atom is approximately 103 kg/m3. The nucleus of an atom has a radius about 10-5 times that of the entire atom, and contains nearly all the mass of the atom. What is the approximate density, in kilograms per cubic meter, of a nucleus?
- 83184kg = 199.7 mg ball-bearing with arcum ference of 26.1 mm wegs 200mg Circumference of a circle = 2nr)? what is the density of the steel in g/cm³ (u of sphere = 4133 A steel 200mg Ⓡ Deng S (mm) Density = D = Di2g 3 D= masse lume S 062994 cm³ 0.66800267 v=4/7| (4:16mm)³_290-4mm 3 mm³ cm Convert + Tr = 4 tr ² 3 0 C = 2115 C = R 211 2994mm² (1 cm )3 26.1mm = 4.16mm 2 x 3.14 10 mm)³ mg-> conuert 200mg 1000g DRAA 0.2For the given A→ draw B→ that will guarantee C = 0.Pd Pd 1. Let's consider a toy model of nuclear fission. Suppose an nucleus of Uranium-235 (92 protons, molar weight of 235 g/mole) "splits" into two "daughter" nuclei of Palladium (46 protons each) – this is not how it really happens, but it's a very simple model that actually gives fairly accurate results. The radius of the original U-235 nucleus is about 7.4 x 10-15 m. (a) If the Pd nuclei each have half the volume of the U nucleus, which is reasonable, and they are "touching" right after the split, how far apart are their centers? (b) Using conservation of energy, what will be the sum of the kinetic energies of the Pd nuclei when they are far apart from each other? (c) That's energy of one atom undergoing fission, so what, then, is the energy released by the fission of 1 kg of U-235? Express this in Joules and also in kilotons of TNT, where 1 kt = 4.2x1012 J. (The Hiroshima bomb yielded about 15 kt) (d) How many kwh (kilowatt-hours) of energy is this, (1 kwh = 3.6x10° J), and (if…