# Problems on Physics

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Work out the following problems. Be sure to show your work in detail. See the hand out uploaded for examples of how the problems should be solved and presented. Â 1. A 55 gal. drum of organic solvent, full and sealed, weighs 400 lbs. The empty drum weights 40 lbs. What is the density of the solvent, in kg/L? What is its specific gravity? Density = p = mass/volume Mass of solvent = 400 lbs 40 lbs = 360 lbs = 360 lbs * (0.45359237 kg/lbs) = 163.29 kg 1 pound = 1 lbs = 0.45359237 kg (online conversion app) Volume of solvent = 55 gallons = 55 gallons * (3.78541178 liters/gallon) = 208.19 L Density = p = mass/volume = 163.29 kg / 208.19 L = 0.784 kg/L (spgr)solvent = p_solvent/p_water Specific gravity of water = p_water = 1000 kg/m^3 = 62 lb/ft^3 Volume of 55 gal drum = Pi*r^2*h where the drum has a 22.5" diameter and is 33.5" high. Thus v_solvent = pi*(11.25)^2*33.5 inches^3 = 13313 in^3 * (1 ft/12in)^3 = 7.7 ft^3 (spgr)solvent = m_solvent/(v_solvent*p_water) = 360 lbs / (7.7 ft^3 * 62 lb/ft^3) = 0.754 The density of the solvent is = 0.784 kg/L and the specific gravity is 0.754. 2. A cylindrical object 0.5m in diameter and 2m long weights has a mass of 200kg. The object is floating end-down in water. How many cm of the object are above the waterline? 0.5m ? cm = how much above waterline? 2m V_sub/V = p_cyl/p_water V_cyl = Pi*r^2*h = pi (0.25m)^2*2m = Pi/8 m^3 P_cyl = mass_cyl/V_cyl = 200kg / (Pi/8 m^3) = 1600/Pi kg/m^3 V_sub/V = p_cyl / p_water =