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- The goal in this problem is to find the growth of an ice layer as a function of time. Call the thickness of the ice layer L. (a) Derive an equation for dL/dt in terms of L , the temperature T above the ice, and the properties of ice (which can leave in symbolic form instead of substituting the numbers). (b) Solve this differential equation assuming that at t=0 , you have L=0 . If you have studied differential equations, you will know a technique for solving equations of this type: manipulate the equation to get dL/dt multiplied by a (very simple) function of L on one side, and integrate both sides with respect to time. Alternatively, you may be able to use your knowledge of the derivatives of various functions to guess the solution, which has a simple dependence on t. (c) Will the water eventually freeze to the bottom of the flask?. A long-distance runner has an average speed of 4 m/s during a race. How far does the runner travel in 20 mm?Verify the normalization equation 0f(v)dv=1 In doing the integral, first make substitution u=m2kBTv=vvp. This "scaling" transformation gives you all features of the answer except for the integral, which is a dimensionless numerical factor. You'll need the formula 0x2e x 2dx= 4 to find the numerical factor and verify the normalization.`
- The power P of a jet of water is jointly proportional to the cross-sectional area A of the jet and to the cube of the velocity v. (a) Write an equation that expresses this variation. (Use k for the constant of proportionality.) P=Akv^3 (b) If the velocity is doubled and the cross-sectional area is halved, by what factor is the power changed?(c) If the velocity is halved and the cross-sectional area is tripled, by what factor is the power changed?(a) Describe in your own words what Biot - Savart Law is.A typical bathroom sink faucet releases about two gallons of water every minute. a) If it takes you 2.5 minutes to brush your teeth and you leave the water run for the entire time, how much water would be used? b) If you only run the water for 30 seconds, how much water would be used?
- Carbon dioxide gas, CO2, travels at about 340 m/s at room temperature. What is the travel rate (velocity) of helium, He, at the same temperature?An interesting problem came up in my research a few weeks ago, and today you will help me solve it! When discussing the change of temperature in a body, one uses the equation: Where Q is the heat (energy) transferred, c is the specific heat of the substance, m is the mass of the substance, and is the change of temperature due to the energy transfer. When I bombard a material with an ion beam, I transfer heat to it through the means of scattering. In my research, I would like to bombard liquid water with an ion beam! Suppose I have 3.45 * 10-13 grams of liquid water, with a specific heat of 4.184 J/gK, and I bombard it with an ion beam with an energy of 10 MeV or 1.602 * 10-12 J. Suppose the water absorbs all the energy of the ion beam, what would be the temperature increase of the sample for each ion bombarded?In 2017 Hurricane Maria dumped nearly 20" of rain on Puerto Rico. Give an order-of-magnitude estimate for the change in po- tential energy of all this rain as it fell from the hurricane.
- A-What are the Catadioptric systemsFind the amount of heat that is required to warm 120 kg of water for you bath by 22 ∘C. Express your answer to three significant figures and include the appropriate units. This is all I was given for this problem, so I am also confused. I'm glad your expert is also confused, makes me feel 10X better.As part of a biology field trip, you have taken an equal-arm balance (Fig. P1. 14) to the beach. Your plan was to measure the masses of various mollusks, but you forgot to bring along your set of Standard gram masses. You notice that the beach is full of pebbles. Although there are variations in color, texture, and shape, you wonder whether you can somehow use the pebbles as a Standard mass set. Develop a procedure for assembling a Standard mass set from the pebbles on the beach. Describe your procedure step by step so that someone else could follow it.