Homework 1-solutions

# Homework 1-solutions - sanchez(es25396 – Homework 1 –...

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Unformatted text preview: sanchez (es25396) – Homework 1 – Stone – (13730) 1 This print-out should have 19 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points A strong lightning bolt transfers about 23 C to Earth. How many electrons are transferred? The charge on an electron is − 1 . 60218 × 10 − 19 C. Correct answer: 1 . 43555 × 10 20 . Explanation: Let : q = 23 C and q e = − 1 . 60218 × 10 − 19 C . The charge is proportional to the number of electrons, so q = n | q e | n = q | q e | = 23 C |− 1 . 60218 × 10 − 19 C | = 1 . 43555 × 10 20 . 002 10.0 points 1) Two uncharged metal balls, X and Y , stand on glass rods and are touching. X Y 2) A third ball, carrying a negative charge, is brought near the first two. X Y − 3) Then the first two balls are separated from each other, X Y − 4) and the third ball is finally removed. X Y When this is all four steps are done, it is found out that 1. Balls Y and X are both negative. 2. Ball Y is positive and ball X is negative. 3. Balls Y and X are both positive. 4. Balls Y and X are still uncharged. 5. Ball Y is negative and ball X is positive. correct Explanation: Basic Concept: Electric induction caused by nearby charges. Solution: When a negative ball is moved near a metallic object ( Y and X ), the negative charge will attract positive charges, causing Y to have excess negative charge and X to have excess positive charge ( Y and X are in contact, so the total net charge on Y and X should be zero). + − − Later, Y and X are separated, retaining their charges, so when the third ball is finally removed, Y will have net negative charge and X will have net positive charge. 003 10.0 points A molecule of DNA (deoxyribonucleic acid) lies along a straight line. It is 1 . 38 μ m long. The ends of the molecule become singly ion- ized; negative on one end, positive on the other. The helical molecule acts as a spring and compresses 1 . 6% upon becoming charged. sanchez (es25396) – Homework 1 – Stone – (13730) 2 The Coulomb constant is 8 . 99 × 10 9 N · m 2 / C 2 . Determine the effective spring constant of the molecule. Take into account the com- pressed length when calculating the distance between the ends of the molecule. Correct answer: 5 . 66805 × 10 − 9 N / m. Explanation: Let : ℓ = 1 . 38 μ m = 1 . 38 × 10 − 6 m , Δ ℓ = 0 . 016 ℓ = 2 . 208 × 10 − 8 m , k C = 8 . 99 × 10 9 N · m 2 / C 2 , and q e = 1 . 60218 × 10 − 19 C . The compressed length is r = ℓ − Δ ℓ = 1 . 35792 × 10 − 6 m and the compression force is F compression = k C q e q e r 2 . The effective force constant is k = F Δ ℓ = k C q 2 e r 2 Δ ℓ = 8 . 99 × 10 9 N · m 2 / C 2 × ( 1 . 60218 × 10 − 19 C ) 2 (1 . 35792 × 10 − 6 m) 2 (2 . 208 × 10 − 8 m) = 5 . 66805 × 10 − 9 N / m ....
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Homework 1-solutions - sanchez(es25396 – Homework 1 –...

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