p201f04-homework01-sol

p201f04-homework01-sol - Version One Homework 1 Heinz 81204...

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Version One – Homework 1 – Heinz – 81204 – Aug 30, 2004 1 This print-out should have 14 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. The due time is Central time. Serway CP 01 03 01:04, trigonometry, multiple choice, > 1 min, fixed. 001 (part 1 of 1) 10 points Consider the expression 2 π s l g , where l is length and g is gravitational ac- celeration in units of length divided by time squared. Evaluate its units. 1. m s 2. s m 3. m 2 4. s 2 5. m 6. s correct 7. m s · 2 8. s m · 2 Explanation: The unit of length ( l ) is m and the unit of gravitational acceleration ( g ) is m s 2 . 2 and π are constants, so the unit of s l g is r m m s 2 = r m ÷ m s 2 = r m · s 2 m = s 2 = s τ = 2 π s l g is the formula for the period of a pendulum (the time for one complete oscillation). Beach Sand 01:05, trigonometry, numeric, > 1 min, nor- mal. 002 (part 1 of 2) 5 points Grains of fine beach sand are assumed to be spheres of radius 35 μ m. These grains are made of silicon dioxide which has a density of 2600 kg / m 3 . a) What is the mass of each grain of sand? Correct answer: 4 . 66945 × 10 - 10 kg. Explanation: Since ρ = m V , then each grain has a mass of m = ρ V = ρ 4 3 π r 3 = ( 2600 kg / m 3 ) 4 3 π (35 μ m) 3 × 1 m 10 6 μ m 3 = 4 . 66945 × 10 - 10 kg . 003 (part 2 of 2) 5 points Consider a cube whose sides are 0 . 15 m long. b) How many kg of sand would it take for the total surface area of all the grains of sand to equal the surface area of the cube? Correct answer: 0 . 004095 kg. Explanation: Each grain of sand has a surface area of A g = 4 π r 2 , and the cube has a surface area of A c = 6 a 2 , so the required number of grains of sand is n = A c A g = 6 a 2 4 π r 2 .
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