solutions_for_chapter_14

# solutions_for_chapter_14 - 14 Picture the Problem The image...

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14. Picture the Problem : The image shows two people talking on a tin can telephone. The cans are connected by a 9.5-meter-long string weighing 32 grams. Strategy: Set the time equal to the distance divided by the velocity, where the velocity is given by equation 14-2. The linear mass density is the total mass divided by the length. Solution: 1. Set the time equal to the distance divided by velocity: d t d v F μ = = 2 . Substitute m d = and insert numerical values: ( 29 ( 29 0.032 kg 9.5 m / 0 8.6 N m d md t d F F = = = = Insight: The message travels the same distance in the air in 0.028 seconds, about 7 times faster. 17. Picture the Problem : Waves travel down two strings, made of the same material and having the same length, but having different diameters and tensions. Strategy: Calculate the ratio of the velocities using equation 14-2. Set the linear mass densities equal to the density of steel times the cross-sectional area of the wires. Solution: 1. Write the ratio of the velocities: A A A A B B B B / / B A v F F v F F = = 2. Write the linear mass density in terms of density and area: A A A B B B B B A A v F A F A v F A F A ρ = = 3. Write the area in terms of the diameter: ( 29 ( 29 2 A A A 2 B B B 2 2 B B A A d v F F d v F F d d π = = 4. Insert the given tensions and diameters: A B 410 N 1.0 mm 2 1.4 820 N 0.50 mm v v = = = ÷ Insight: The ratio of the velocities is proportional to the square-root of the tensions and inversely proportional to the diameters.

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31. Picture the Problem : The figure shows a person throwing a rock down an 8.85-m deep well. The sound of the splash reaches the
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solutions_for_chapter_14 - 14 Picture the Problem The image...

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