If M = mass of wire, f= density of wire, R = radius of wire, r= change in radius. L = oeiginal L = original length of wiret 1= change in length, then Poiss on ratio is given as - Mrf Mr Mr Mr f (2) TUR³l TR²LP TIR³ fl TR²l
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- how to determine volume with of a zinc rod with only the mass, length and diameter, when the mass is 69.5 grams and the length is 34.3 and the diameter is 19?A cell membrane is 4.81 nm thick. How thick is it in inches?Calculating the Number of Molecules in a Cubic Meter of GasHow many molecules are in a typical object, such as gas in a tire or water in a glass? This calculation can give us an idea of how large N typically is. Let’s calculate the number of molecules in the air that a typical healthyyoung adult inhales in one breath, with a volume of 500 mL, at standard temperature and pressure (STP), which is defined as 0 ºC and atmospheric pressure. (Our young adult is apparently outside in winter.)StrategyBecause pressure, volume, and temperature are all specified, we can use the ideal gas law, pV = NkB T, to find N
- There is relatively little space between atoms in solids and liquids, so that the average density of an atom is about the same as matter on a macroscopic scale - approximately 10^3 kg/m^3. The nucleus of an atom has a radius of about 10^-5m of that of the entire atom, and conatins nearly all mass of the atom. a) What is the approximate density, in kilograms per cubic meter, of a nucleus. b) One possible remnant of a supernova, called a neutron star, can have the density of a nucleus, while being the size of a small city. What would be the raduis, in kilometers, of the neutron star with a mass 10 times that of the Sun? The radius of the Sun is 7*10^8 m and its mass is 1.99*10^30 kgHow many minutes does IH take to fll a 36 gallon bathtub if the faucet opening has an area of 1.2 cm2 and water flows out of it at 3.2 mis? li gal = 3.785 L = 3.185 x103 m³)(1) A metallic sphere has a density p and a radius r. (a) Using dimensional analysis, derive a formula for the mass of the sphere. (b) Using dimensional analysis, derive a dependence of the sphere radius if its mass and density are known.
- derive the second equation from the firstShow calculations of the volume, density,and %error Density =8.2Consider a water tank that is being filled with rainfall at the top and is drained through a small hole atthe bottom. The change in volume can be modelled by considering the amount of water entering andleaving the tank (per unit of time) as followsdVdt= fin − fout.Here volume of water in the tank V is in litres, flow rate in fin is in litres per hour, flow rate out fout isin litres per hour and time t is in hours. Initially, the tank contains 50L of water: V (0) = 50.(a) Assume the rainfall throughout the day is getting heavier, such that, fin(t) = 10 + t andthat the tank is losing 10% of its volume of water per hour, such that, fout(V ) = 0.1V . Check bydirect substitution that the functionV (t) = 10(t + 5e−0.1t)satisfies the ODE and the initial condition.Now assume that the hole is slowly growing in size, so that the flow rate out increaseswith time:fout(V, t) = 0.1(1 + 0.1t)V.Solve the ordinary differential equation for V (t) with this flow rate out, using either separation…