2-1 UArk graduate student Justin Trimble made the front page of last Sunday's NWArk Times when he complained that he must look both ways before crossing the railroad tracks. Mr. Trimble, it seems, is one of 410 people who cross the tracks on Razorback Road each day, and he thinks there needs to be a crossing signal to warn traffic of the one train per day that travels that spur line, at an expense to the city or state of $150,000 or more. Railroad Safety Tips, printed in the Times, state dramatically how hard it is to stop a moving train.

Postscript: After this problem was written, Sunday’s news story became the subject of an editorial in yesterday’s paper.

Given:  The Times states that "a freight train moving at 55 mph can take a mile or more to stop once the emergency brakes are applied." We all know that a mile is 5,280 ft, exactly, just as a foot is exactly 12 inches. An inch is defined, by act of Congress, as exactly 2.54 cm.

Find (a)  What's a mile? Answer should be in km and  to the proper number of significant figures. (1.609344 km)

(b)     Express the speed of the freight train in m/s. (24.6 m/s)

(c)     What is this deceleration, in SI units, of a freight train? (0.188 m/s^2 is acceptable but  0.2 m/s^2 is better)

5-B9 (Somewhat revised to cover Chapter 6 as well as Chapter5.)  ..One way of measuring the muzzle velocity of a bullet is to fire it horizontally into a massive block of wood placed on a cart. Assuming no friction, we then measure the velocity with which the wood (containing the bullet) starts to move.

Given:   .The bullet has a mass of 50 g. The wood and its cart has a mass of 15 kg. The cart, wood and bullet travel 0.8 m in 0.45 s, traveling together after the shot.

Find (a)  What is the final velocity of the cart, wood and bullet? (1.77 m/s or 1.8 m/s)

       (b)  What is the final kinetic energy of the system? (24 J)

(d)     What is the final momentum of the system? (27 kg m/s)

(e)     What is the initial velocity of the bullet before entering the wood?  (535 m/s or 500 m/s)

(f)      How much energy is lost upon impact? (7.1 kJ)

11-1 An exam room is a quiet place. So quiet that people talking out in the hallway make noise many times louder than all the folks in the room working at their exam.

Given: The sound intensity level of people taking the exam is 56 dB, whereas one person out in the hallway, talking in normal tones produces about 66 dB. If a group of 4 people out in the hallway talk at the same time, there will be proportionally more sound energy produced.

Find: (a) By what fraction is sound energy in the room increased if one person out in the hallway starts talking? (10)

(b) What is the sound level intensity of  the group of people talking all at the same time? (72 dB)

12-1. A metal crown seems to weigh less under water than in air because of the buoyant force of the water.

Given: A crown weighed in air weighs 50 N, while the same crown under water seems to weigh only 44 N.

Find: (a) What is the buoyant force acting on the crown? ( 6N)

  (b) What is the volume of water displaced? (0.61 L)

  (c) Calculate the density of the metal with which the crown is made. (8.3 kg/L)

15-B13(Somewhat revised, but the numbers are the same.) A cylindrical diving bell with an open bottom is lowered in a fresh water lake one day with a diver inside. The diver sees the level of the water inside the bell rise.

Given:  . The bell is 4 m tall and the water rises to within 1 m of the top. Atmospheric pressure is 100 kPa that day.

Find: (a)  What is the pressure inside the bell? (400 kPa)

(b)  How deep is the bell in the lake? (30.6 m Remember to use gage pressure, not absolute pressure, to calculate depth in a fluid.)

17-1. Experimental engines have been developed, not so much for practical purposes, but just to see how close we can get to converting all of the heat from a hot place into mechanical energy. The trick is to minimize the heat that must be dumped into the cold place, usually called a heat sink.

Given: One experimental engine operated between a heat source at 1,727°C and a heat sink at 427°C. Even at these temperatures, for every 1000J of heat from the heat source, 600J of heat goes into the heat sink.

Find: (a) What is the maximum theoretical efficiency of this engine? (65 %)

(b) What efficiency did the engine actually produce? (40 %)