Posted by Larry King on Thursday, February 5, 2009 at 6:05pm.
Dear Sir,
Please help. I am struggling with the below problems for a very long time.
thanks
Larry King
1) Suppose that in a certain atmospheric situation, a falling raindrop, having an initial mass of 0.010g. collects smaller droplets by collision at such a rate that, after 10s, it has a mass of 0.020g g and a diameter of 3.4 mm.
(a) If the droplet continues to gain mass at the same average rate as it continues to fall, what will its diameter at the end of the next 10 s? (Using a scale and ratio reasoning, not substitution in formulas, and explain what you are doing.)
(b) If 3.4 mm a reasonable or unreasonable order of magnitude for the diameter of a droplet with a mass of 0.020g? ( Make a crude, quick estimate- not an elaborate calculation- and explain your reasoning)
2 ) A statue is to be scaled down, without distorting its shape, by changing its total volume from 1.25m3 . Explain your reasoning in each of the following calculations.
(a) If the height of the original statue is 250cm, calculate the height of the smaller model.
(b) If the circular base of the original statue has a circumference of 45 cm, calculate the circumference of the scaled-down base in the smaller model.
(c) How will the total surface area of the model compare (this means an appropriate ratio) with the total surface area of the original? How will the surface areas of the circular bases compare?
(d) If both the model and the original are made of the same material, how will the mass of model compare with mass of the original?
(e) If the model and the original are not made of the same material, what would you have to know about the materials to be able to compare the masses, and how would you use this information?
(f) If the original statue and the model turned out to have the same mass, what would you conclude about the materials making up the two objects? (Give a numerical answer comparing relevant properties of the materials.)
2) As a first approximation, let us think of an older person O as being a larger scale model of a younger person Y, with lengths in all parts of the body increased by the same scale factor. Suppose the weight of O is 4.50 times the weight of Y.
(a) If height of O is 6.0 ft, what must be the height of Y?
(b) How will the cross-sectional area at some level in the legs of the older person compare with the cross-sectional area at the corresponding level in the legs of the younger?
(c) Will the compressional stress on the leg bones be the same in the two individuals? (“Stress” is the name for the force per unit area that the bone must support.) Why or why not? If not, for which individual will the stress be greater? By what numerical factor? It is because of the effect that emerges in the analysis you have just conducted that larger animals are, in reality in the world around us, not simply scaled-up models of smaller animals. Explain the reasoning behind this statement.
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