Page 70 - Fisika Terapan for Engineers and Scientists

270 CHAPTER 8 Conservation of Energy

Checkup 8.2 Checkup 8.4

1. The number of turning points must decrease with increasing 1. Yes; the Sun continually loses mass in the form of heat and
energy [we do not consider a stationary point of stable light, as well as by emitting particles with mass.
equilibrium (Fig. 8.8), since the particle is moving]. Consider 2. Energy and mass are both conserved; the original rest mass is
the potential of Fig. 8.7: for small energies, the particle will converted to the energy of the light (electromagnetic radia-
move back and forth (two turning points); for somewhat tion), and this light carries away mass as well as energy.
higher energy, the particle will move back from the left end
3. (A) Increase. The mass of the water will increase by the usual
but escape from the right end (one turning point). Unless U 2

m
E/c , where
E is the increase in thermal energy of
, for sufficiently high energy the particle could escape from
the water.
the left end also (no turning point). In one dimension, there
cannot be more than two turning points, although the two
turning points will of course be different for different Checkup 8.5
energies.
1. (a) No; there is no force parallel to the motion, so there is no
2. The maximum speed corresponds to the deepest part of the
work done and no power expended. (b) Trotting uphill, you
curve (maximum kinetic energy, K E U); from the figure,
deliver power at a rate P Fv mg sin v, where m is the
this occurs at x 6 m. The maximum acceleration and force
mass of the pack, is the angle of the incline, and v is the
(F dU/dx) occurs where the slope is largest; for the
speed along the incline. (c) Trotting downhill, the component
bungee jumper, this is at x 15 m.
of F along v is negative, so you do negative work on the back-
3. (B) 2. The potential-energy curve of the spring force is a
pack; that is, the backpack delivers power to you.
simple parabola (Fig. 8.1), so there are two turning points for
2. Yes, the energy you have to expend is mgh, whichever slope of
any positive energy.
road you take. The steeper road requires more of an effort,
since, for example, for the same walking speed, the force is
Checkup 8.3 more nearly parallel to the velocity, and so the power
.
expended, P F v, is greater.
1. No. Gravitational potential energy is lost as the parachutist
3. Some of the power is lost as heat, due to the friction force
descends (at uniform speed, there is no change in kinetic
between the boat and the water; some of the energy is con-
energy). From a macroscopic viewpoint, the energy lost due to
verted into a more macroscopic kinetic energy of the water, by
friction with the air is converted into heat.
the generation of water waves.
2. The energy comes from a decrease in the chemical energy of
4. (C) 4. The power is equal to the force times the speed. At the
the exploding gunpowder; microscopically, such chemical
same speed, a car with twice the mass will require twice the
energy comes from changes in the kinetic and potential energy
power to move against gravity; if that car is also traveling at
of electrons in the atoms and bonds of the elements involved.
twice the speed, it will then require four times as much power
3. The energy is converted to heat due to frictional forces; these
(ignoring other losses).
may include friction in the engine, brakes, tires, and road, as
well as air friction.
4. (C) The kinetic energy is converted into heat due to frictional
forces, mostly in the brakes (brake pads rub against drums or
disks), partly where the tires contact the road, and some from
air friction. All the heat is eventually transferred to the air as
the brakes, tires, and road cool.