MA 1135 Practice Test III (answers on last page) Tuesday, April 16, 2013

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1 MA 35 Practice Test III (answers on last page) Tuesday, April 6, 203 Name Note: Test III is Thursday (4/8/3). Big Note: Bring your calculators, no computers for this test. I m going to restrict you to the conversions in the table below, and I m going to want to see your work. For example, to convert 07 inches into feet, I d like to see () 07 inches 5280 feet = mile 2 inches = 60 minutes = hour 60 seconds = minute 6 ounces = pound 6 fluid ounce = pint 2 pints = quart 4 quarts = gallon 3 = 7.48 gallons = meters 2.54 centimeters = inch 000 millimeters = meter 00 centimeters = meter 2.2 pounds = kilogram 000 grams = kilogram 2000 pounds = ton quart = liters cubic meter = meter 3 = 000 liters centimeter 3 = milliliter acre = square feet = 8.92 feet. 2 inches Homework. Convert 6 feet into meters. 3. Convert 600 meters into miles. Homework 2. Convert a speed of 30 miles per hour into meters per minute. 3. Gasoline has a density of pounds per pint. Convert this to grams per liter. 5. According to Wikipedia, the density of air is about.225 kilograms per cubic meter. Convert this to ounces per pint.

2 MA 35 Practice Test III (answers on last page) 2 Homework 3. An acre is a measure of area, so an acre-foot is a measure of volume (like a swimming pool with surface area equal to an acre and one foot deep). Using only the formulas listed below, convert one acre-foot to gallons. (Convert acres to square feet, then cubic feet to gallons.) You ll start (2) acre foot feet2 acre 2. An Olympic-size swimming pool is 50 meters long. Each lane is 2.5 meters, so with eight lanes, we d need a width of 20 meters (actually a bit more, but let s go with 20 meters). For simplicity, let s go with a single depth of 2 meters. a. How many cubic meters of water would fill the pool? b. Convert this to cubic feet. Note that (3) meters c. Now convert this to gallons meters d. Instead of gallons, convert to acre-feet meters = meters 3 = meters 3. e. Assuming that a gallon of water weighs 8 pounds, how many pounds of water are in the pool? f. What is that in tons? 3. I ve got some gravel, which when piled up, has a dry density of ρ dry = 2.24 grams per cubic centimeter and a porosity of n = a. The dry density tells you how much a cubic centimeter of dry gravel weighs in grams. Convert the dry density to kilograms per cubic meter. b. If you filled the swimming pool in Problem 2 with gravel, how much would that gravel weigh in kilograms? c. How much is that in pounds? d. How much is that in tons? e. With the pool filled with dry gravel, how much water could you put in? Express your answer in cubic meters. Homework 4. Remember that an acceleration of g is feet (4) g = 32 second 2. How many g s would an acceleration of 6 feet per second per second be? miles per hour is the same as 88 feet per second. Traffic engineers assume that in a panic stop situation, a car can decelerate at 5 feet per second per second. This would probably help you to determine how long a traffic light will stay yellow. a. If you re driving 60 miles per hour, and you slam on your brakes, and manage to stop in 6 seconds, what is your acceleration (or deceleration, if you wish)? That is, how much speed must you decrease each second? b. What is that in g s?

3 MA 35 Practice Test III (answers on last page) 3 3. Find the following values on your calculator. a. sin(30 ). d. cos(5 ). e. tan(2 ). 4. Find the slope and percentage grade. a. Horizontal distance: 50 feet. Vertical distance: 2 feet. d. Angle of inclination: 3. Homework 5 In the following, you re given two of x, y, R, θ, and m. Find the other three.. x = 77 feet and y = 2 feet. 3. m = 6% and x = 45 feet. 4. m = and x = 80 feet. 5. θ = 5 and x = 225 feet. Homework 6 For all of the following, find the angle of inclination, if necessary, the perpendicular, parallel, and slide forces, and then answer the question posed.. I have some sticky climbing shoes (not really), which have a coefficient of friction of µ =.42 on granite. I weigh 65 pounds. Can I stand on a 50 granite slope? 3. Can a 3500 pound car be parked on a wet 25% grade with coefficient of friction µ = 0.20? 4. I weigh 65 pounds. Can I stand on an 8:2 pitched roof, where my shoes on the shingles have a coefficient of friction of µ = 0.68? Note: An 8:2 pitch is the same as a slope of m = 8 2. Answers on next page.

4 MA 35 Practice Test III (answers on last page) 4 -) 6 feet meters =.83 meters (corrected 9:30am 4/6/3). -3) 600 meters foot meters mile = miles feet 2-) 30 miles 5280 hour feet mile meters hour 60 minutes = meters per minute 2-3) pounds pint kilogram 000 grams 2.2 pounds kilogram 2 pints quart quart = grams per liter liters 2-5).225 kilograms cubic meter cubic meter 000 liters 3-) acre foot liters quart quart 2.2 pounds 6 2 pints ounces = ounces per pint. kilogram pound feet gallons acre = gallons a) V = 50 meters 20 meters 2 meters = 2000 meters 3. b) 2000 meters 3 c) feet 3 d) feet feet 2 e) gallon 8 pounds gallon meters 3 = feet gallons 3 = gallons. acre feet 2 =.6225 acre-feet. = pounds. f) pounds ton = tons pounds grams 3-3a) 2.24 centimeter kilograms. meter 3 b) 2000 meters 3 c) kilograms (00 centimeters)3 ( meter) 3 kilogram 000 grams = 2.24 grams centimeter centimeters 3 meter 3 kilogram 000 grams = 2240 kilograms meter 3 = kilograms. 2.2 pounds = pounds. kilogram d) pounds ton = 4928 tons pounds e) Porosity: n = V pore space 2000 meters 3 = 0.20, so Vpore space = meters 3 = 400 meters 3. 4-) 0.5 g. 4-2a) 88 feet second 6 seconds = 4.67 feet. second 2 4-2b) 4.67/32 = g. 4-3a) 0.5, d) 0.966, e) a) m = 2 50 = 0.08 = 8%. d) m = tan(3 ) = = 5.2%. 5-) R = = feet. m = 2 77 = 0.56 = 5.6%. θ = tan (0.56) = ) y = = 8.7 feet. R = = feet. θ = tan (0.06) = ) y = = 6 feet. R = = feet. θ = tan (0.075) = ) m = tan(5 ) = = 8.7%. y = = 9.58 feet. R = = feet. 6-) Fperp = 65cos(50 ) = pounds, Fpar = 65sin(50 ) = pounds, F slide = = 50.6 pounds. I won t slide, so yes, I can stand on the slope.

5 MA 35 Practice Test III (answers on last page) 5 6-3) m = θ = tan (0.25) = Fperp = 3500 cos(4.04 ) = pounds, Fpar = 3500 sin(4.04 ) = pounds, F slide = = pounds. It will slide, so no, we can t park the car there. 6-4) m = 8 2 = θ = tan (0.667) = Fperp = 65 cos(33.7 ) = pounds, Fpar = 65 sin(33.7 ) = 9.55 pounds, F slide = = pounds. I won t slide, so yes, I can stand on the slope, but just barely.