Physics: Principles with Applications (7th Edition)

Published by Pearson
ISBN 10: 0-32162-592-7
ISBN 13: 978-0-32162-592-2

Chapter 6 - Work and Energy - Search and Learn - Page 169: 2

Answer

a) Energy from decreasing potential energy is converted into heat, not kinetic energy. b) Yes c) Generated heat is divided into the break chamber and the engine d) $E_{th}=-8.28\times10^6J$

Work Step by Step

a) When the truck is going down a steep hill, if it does not apply its brakes, its speed will increase as more time passes. With the brakes on, the speed will stay constant but there will still be excess energy as the potential energy will decrease while kinetic energy remains constant. All this extra energy is turned into heat, which over time will continue to increase and be enough to start a fire. If the steepness of the hill is higher than the rate of change in energy, power dissipation is also higher. To control the truck's speed, we can better control its speed. This, with the use of brakes can help control the truck's speed. b) Yes, it would matter. If the two hills are the same height, the initial potential energy is the same. In case of a gradual hill, it will take longer for the same amount of heat to dissipate. In other words, the power output will be smaller and the break chamber will not heat up as much. c) By switching to a lower gear, the heat can be dissipated through both the engine and break chamber so the breaks won't get as hot. Also, the engine has other cooling mechanisms which could help cool the truck. d) $v_i=95\frac{km}{h}=26.39\frac{m}{s}$ $v_f=35\frac{km}{h}=9.72\frac{m}{s}$ $d=360m$ $E_{th}=\frac{m(v_f^2-v_i^2)}{2}-mg(h_f-h_i)$ $=\frac{(8000kg)((9.72\frac{m}{s})^2-(26.39\frac{m}{s})^2)}{2}-(8000kg)(9.8\frac{m}{s^2})(360m\sin(12^o))$ $=-8.28\times10^6J$
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