Clayton College & State University August 28, 2002 Name 1. The height of horses is measured in a unit called hands. If a height of 20 hands were expressed in the SI system of units, the units would be: a. m. Yes, this is the right answer since we are talking about length b. s. c. m/s. d. kg/s. 2. Which of the following equations is dimensionally consistent? a. t =1/3 xa. No, T =L*L/T 2, T =L 2 /T 2 b. v = ½ at 2. No, L/T =L/T 2 *T 2, L/T =L c. a=(vt 2 ) 1/2. No, L/T 2 =L 1/2 *T d. v 2 = 2ax. Yes, L 2 /T 2 = L/T 2 *L, L 2 /T 2 = L 2 /T 2 3. The US dollar is not an SI unit. Nonetheless, express the sticker price of your favorite sports car in kilodollars (kilobucks!). What is the cost per kilogram? 30,000 dollars = 30.0 * 10 3 dollars = 30.0 kilodollars My estimation of the mass of a car: 2000 kg. Cost per kilogram = 30,000 dollars/ 2000 kg = 15.0 dollars/kg.
Clayton State University August 29, 2005 Name SOLUTION 1. Hydraulic engineers in the United States often use, as a unit of volume of water, the acrefoot. If a volume of 25.0 acre-feet were expressed in the SI system of units, the units would be: a. m 3. b. 1/s. c. m 2 -kg. d. kg/s. 2. Given that a = 1.50 m and c = 4.00 m, find: a 2 + b 2 = c 2 b 2 = c 2 - a 2 b = (c 2 - a 2 ) 1/2 a. The length of side b. b = ((4.00 m) 2 (1.50 m) 2 ) 1/2 = 3.71 m b. The sine of angle sin() = a/c = (1.50 m) / (4.00 m) = 0.375
c. The tangent of angle tan() = a/b = (1.50 m) / (3.71 m) = 0.404 d. Angle = tan -1 (0.404) = 22.1 o Clayton State University August 28, 2006 Name SOLUTION x = A v A = x/v 1. If the displacement of the object, x, is related to velocity, v, according to the relation x = A v, the constant, A, has the dimension of which of the following? a. Acceleration. b. Length. c. Time. d. Area. A = [L]/([L]/[T]) = [T] 2. The kilogram is currently defined as a. The mass of a platinum iridium cylinder kept in Sevres, France. b. The mass of 5.9786332 x 10 26 protons.
c. The mass of one liter of pure water. d. The mass of a cube of pure water, 10 cm on each side, at standard temperature. 3. The Hope diamond weighs 44.5 carats. There are 200 mg per carat. How many kilograms does the Hope diamond weigh? a. 0.000890 kg. b. 0.00890 kg. c. 0.0890 kg d. 0.890 kg. (44.5 carats)(200 mg/carat) = 8900 mg 8900 mg = 8900 x 10-3 g = 8.900 g (8.900 g)(1 kg/1000g) = 0.008900 kg Clayton State University August 27, 2007 Name SOLUTION 1. If the displacement of the object, x, is related to time, t, according to the relation x = A t, the constant, A, has the dimension of which of the following? a. Acceleration. b. Velocity. c. Time. d. Length.
2. The meter is currently defined as a. The distance between two etched lines in a platinum-iridium bar kept in Serves, France. b. One ten-millionth of the distance between the North Pole and the equator. c. The distance traveled by light in 1/299,792,458 of a second. d. 1,553,146.1 wavelengths of red cadmium light in dry air at 25 o C. 3. Given that a = 3.50 m and b = 6.50 m, find: c 2 = a 2 + b 2 c = (a 2 + b 2 ) 1/2 a. The length of side c. c = ((3.50 m) 2 + (6.50 m) 2 ) 1/2 = 7.38 m b. The tangent of angle tan = a/b = (3.50 m)/(6.50 m) = 0.538 c. The angle = tan -1 (0.538) = 28.3 o
Clayton College & State University January 14, 2004 Name SOLUTION 1. Hydraulic engineers in the United States often use, as a unit of volume of water, the acre-foot. If a volume of 25.0 acre-feet were expressed in the SI system of units, the units would be: a. m 3. b. 1/s. c. m 2 -kg. d. kg/s. 2. Given that a = 2.00 m and c = 5.00 m, find: a. The length of side b. c 2 = a 2 + b 2 b 2 = c 2 - a 2 b = (c 2 - a 2 ) ½ b = ((5.00 m) 2 (2.00 m) 2 ) ½ = (21.0 m 2 ) 1/2 = 4.58 m b. The sine of angle sin(q) = a/c = (2.00 m) / (5.00 m) = 0.400
c. The tangent of angle tan () = a/b = (2.00 m)/ (4.58 m) = 0.436 Clayton State University January 18, 2006 Name _SOLUTION 1. The base SI unit of time is a. Hour. b. Minute. c. Second. d. Millisecond. 2. Given that a = 1.50 m and b = 3.00 m, find: a 2 + b 2 = c 2 a. The length of side c.
c = (a 2 + b 2 ) 1/2 c = ((1.50 m) 2 + (3.00 m) 2 ) 1/2 = 3.35 m b. The cosine of angle cos() = b/c = (3.00 m) / (3.35 m) = 0.894 c. The tangent of angle tan() = a/b = (1.50 m) / (3.00 m) = 0.500 d. Angle = tan -1 (0.500) = 26.6 o Clayton State University January 17, 2007 Name SOLUTION 1. If you are measuring the length of the room, the most appropriate SI unit is a. Kilometer. b. Meter. c. Centimeter. d. Millimeter. 2. The density of a solid object is defined as the ratio of the mass of the object to its volume ( = m/v). The dimension of density is a. [M]/[L].
b. [L] 3 /[M]. c. [M][L] 2. d. [M]/[L] 3. 3. 3. Given that a = 1.50 m and c = 3.00 m, find: b = (c 2 - a 2 ) 1/2 a. The length of side b. b = ((3.00 m) 2 (1.50 m) 2 ) 1/2 = 2.60 m b. The tangent of angle tan = a/b = (1.50 m)/(2.60 m) = 0.577 Clayton State University January 14, 2008 Name SOLUTION 1. If the velocity of the object, v, is related to time, t, according to the relation v = A + B t, the constant, A, has the dimension of which of the following? a. Acceleration. b. Velocity.
c. Time. d. Length. 2. The kilogram is currently defined as a. The mass of a platinum-iridium cylinder kept in Sevres, France. b. The mass of 5.9786322 x 10 26 protons. c. The mass of one liter of pure water, free of air, at standard temperature and pressure. d. The mass of a cube of pure water, free of air, 10.0 cm on each side, at standard temperature and pressure. 3. Given that a = 1.40 m and c = 3.50 m, find: a. The length of side b. a 2 + b 2 = c 2 b = (c 2 - a 2 ) 1/2 b = ((3.50 m) 2 - (1.40 m) 2 ) 1/2 = 3.21 m b. The cosine of angle cos = b/c = (3.21 m)/(3.50 m) = 0.917 c. The angle = cos -1 (0.917) = 23.5 o
Clayton College & State University May 20, 2004 Name SOLUTION 1. If the displacement of the object, x, is related to velocity, v, according to the relation x = A v, the constant, A, has the dimension of which of the following? a. Acceleration. b. Length. c. Time. d. Area. L = [A] x L/T [A] = L/ (L/T) = T 2. On planet Q the standard unit of volume is called guppi. Space travelers from Earth have determined that one liter = 38.2 guppies. How many guppies are in 150 liters? a. 5730 guppies. 150 liters x (38.2 guppies/1 liter) = 5730 guppies b. 0.255 guppies. c. 3.93 guppies. d. 188 guppies. 3. Express 1.00 microcentury in more conventional units. 1.0 microcentury = 10-6 century = (10-6 ) (100 years) = 10-4 years
Clayton College & State University June 6, 2005 Name SOLUTION 1. The height of horses is measured in a unit called hands. If a height of 20 hands were expressed in the SI system of units, the units would be: a. m. b. s. c. m/s. d. kg/s. 2. Which of the following equations is dimensionally consistent? a. t =1/3 xa. T = L(L/T 2 ) incorrect b. v = ½ at 2. L/T = (L/T 2 )(T 2 ) incorrect c. a=(vt 2 ) 1/2. (L/T 2 ) = [(L/T) (T 2 )] 1/2 incorrect d. v 2 = 2ax. (L/T) 2 = (L/T 2 )L CORRECT 3. Given that a = 2.00 m and b = 4.00 m, find:
a. The length of side c. c 2 = a 2 + b 2 c 2 = (2.00 m) 2 + (4.00 m) 2 = 20.0 m 2 c = (20.0) 1/2 m b. Sine of angle sin = a/c = [2.00 m]/[(20.0) 1/2 m] = 2.00/(20.0) 1/2 c. Tangent of angle tan = a/b = (2.00 m)/(4.00 m) = 0.500 d. Angle. tan -1 (0.500) = 26.6 o
Clayton State University June 4, 2007 Name _SOLUTION 1. Solve for x: (2.5 x + 5) 1/2 = 4 2.5 x + 5 = 16 2.5 x = 11 x = 4.40 2. Solve for t: 3 t 2 8t + 15 = 0 t 1,2 = 8 +/- (8 2-4(3)(15)) 1/2 t 1,2 = 8 +/- (-116) 1/2 No real solutions 3. 3. Given that a = 1.50 m and b = 2.50 m, find: c 2 = a 2 + b 2 a. The length of side c.
c = (a 2 + b 2 ) 1/2 c = ((1.50 m) 2 + (2.50 m) 2 ) 1/2 = 2.92 m b. The sine of angle sin = a/c = (1.50 m)/(2.92 m) = 0.514 c. The angle = sin -1 (0.514) = 31.0 o 4. Which one of the lines below has a negative slope? The one in the upper left corner.