Homework 1-solutions

Homework 1-solutions - kaplan(hmk378 Homework 1...

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kaplan (hmk378) – Homework 1 – Weathers – (17104) 1 This print-out should have 9 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points The mass of the planet Saturn is 5 . 64 × 10 26 kg and its radius is 6 × 10 7 m. Calculate its density. Correct answer: 623 . 357 kg / m 3 . Explanation: Let : M = 5 . 64 × 10 26 kg and R = 6 × 10 7 m . Assuming Saturn to be a sphere (neglecting the rings), we can use the formula for the volume of a sphere of radius R : V = 4 3 π R 3 . The density of Saturn is ρ = M V = M 4 3 π R 3 = 3 (5 . 64 × 10 26 kg) 4 π (6 × 10 7 m) 3 = 623 . 357 kg / m 3 . 002 10.0 points This problem shows how dimensional analysis helps us check and sometimes even find a formula. A rope has a cross section A = 8 . 13 m 2 and density ρ = 1800 kg / m 3 . The “linear” density of the rope μ , defined to be the mass per unit length, can be written in the form μ = ρ x A y . Based on dimensional analysis, determine the powers x and y by choosing an expression below. 1. μ = ρ A 2. μ = 1 ρ A 2 3. μ = ρ A 2 4. μ = A ρ 2 5. μ = ρ A correct 6. μ = ρ A 2 7. μ = 1 ρ A 8. μ = A 2 ρ 9. μ = A ρ 10. μ = A 2 ρ 2 Explanation: Kilogram (kg): a unit of mass ( M ). Meter (m): a unit of length ( L ). [ x ] means ”the units of x ”. The units of both sides of any equation must be the same for the equation to make sense. The units of the left hand side (LHS) are given as [ μ ] = M L = ML 1 , and the right hand side has [ ρ x A y ] = parenleftbigg M L 3 parenrightbigg x × ( L 2 ) y = M x L 3 x L 2 y = M x L 2 y
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