Homework Solutions 9 - homework 05 – ASH, BEN – Due:...

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Unformatted text preview: homework 05 – ASH, BEN – Due: Feb 14 2008, 9:00 pm 1 Question 1, chap 1, sect 6. part 1 of 1 10 points Consider a piece of string which is placed along the x-axis. Let Δ m be the mass of a segment of the string and Δ x the length of this segment. The linear mass density, μ , of a piece of string is defined as μ = Δ m Δ x . Denote ρ to be its mass density defined as ρ = mass volume and A its cross sectional area. Let us write μ = ρ x A y . Using dimensional analysis, determine the equations which enable one to solve for x and y . 1. x = 1 , 2 y + 3 x = − 1 2. x = 1 , 2 y − 3 x = 1 3. x = 1 , 3 x + 2 y = 1 4. x = − 1 , 2 y − 3 x = − 1 5. x = − 1 , 2 y + 3 x = − 1 6. x = − 1 , − 2 y − 3 x = − 1 7. x = 1 , 2 y − 3 x = − 1 correct 8. x = 1 , − 2 y − 3 x = − 1 9. x = − 1 , 2 y − 3 x = 1 10. x = − 1 , 3 x + 2 y = 1 Explanation: [ μ ] = [ ρ x A y ] ML − 1 = M x L − 3 x L 2 y = M x L 2 y − 3 x Equating both sides yields the equations x = 1 , 2 y − 3 x = − 1 Question 2, chap 1, sect 1. part 1 of 1 10 points Two points in a rectangular coordinate sys- tem have the coordinates (7 . 7 cm, 4 . 3 cm) and ( − 8 . 7 cm, 3 . 4 cm). Find the distance between these points. Correct answer: 16 . 4247 cm (tolerance ± 1 %). Explanation: Given : x 1 = 7 . 7 cm , y 1 = 4 . 3 cm , x 2 = − 8 . 7 cm , and y 2 = 3 . 4 cm . Using the Pythagorean Theorem, d = radicalBig (Δ x ) 2 + (Δ y ) 2 = radicalBig ( x 2 − x 1 ) 2 + ( y 2 − y 1 ) 2 = radicalBig [7 . 7 cm − ( − 8 . 7 cm)] 2 + (3 . 4 cm − 4 . 3 cm) 2 = 16 . 4247 cm . Question 3, chap 2, sect 2. part 1 of 1 10 points Ann is driving down a street at 51 km / h. Suddenly a child runs into the street. If it takes Ann 0 . 785 s to react and apply the brakes, how far will she have moved before she begins to slow down? Correct answer: 11 . 1208 m (tolerance ± 1 %). Explanation: d = v t = (51 km / h) (0 . 785 s) = 11 . 1208 m . homework 05 – ASH, BEN – Due: Feb 14 2008, 9:00 pm 2 Dimensional analysis for d : km h · s 1 · 1 h 3600 s · 1000 m 3600 km = m Question 4, chap 2, sect 2. part 1 of 1 10 points The graph shows position as a function of time for two trains ( A and B ) running on par- allel tracks. At time t =0 the starting position of both trains are at the origin (position zero). time position t p A B Which is true: 1. Both trains have the same velocity at some time before t p . correct 2. Both trains speed up all the time. 3. Both trains slow down all the time. 4. In the time interval from t =0 to t = t p , train B covers more distance than train A. 5. In the time interval from t =0 to t = t p , train A covers more distance than train B. 6. Somewhere before time t p , both trains have the same acceleration....
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This note was uploaded on 09/29/2008 for the course PHY 303 taught by Professor Erskine/tsoi during the Spring '08 term at University of Texas at Austin.

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Homework Solutions 9 - homework 05 – ASH, BEN – Due:...

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