What is the block’s kinetic
energy at the bottom?
Wnc = EfíEi
(Fcosș)ǻx = KEfíPEi
KEf = PEi + (F cos șǻx)
KEf = (mgh) + (F cos șǻx)
KEf = (1.00 kg × 9.80 m/s^2 × 2.00 m) +
(2.00 N × cos 180° × 6.00 m)
KEf = 19.6 J + (í12.0 J)
KEf = 7.60 J
6.21 - Gotchas
You are asked to push two wheelbarrows up a hill. One wheelbarrow is empty, and you are able to push it up the hill in one minute. The other
is filled with huge rocks, and even after you push it for an hour, you cannot budge it. In which case do you do more work on the wheelbarrow?
You do more work on the empty wheelbarrow because it is the only one that moves. You do no work on the wheelbarrow filled with rocks
because you do not move it; its displacement is zero.
Two 1/4 kg cheeseburgers are moving in opposite directions. One is rising at three m/s, the other is falling at three m/s. Which has more kinetic
energy? They are the same. The direction of velocity does not matter for kinetic energy; only the magnitude of velocity (the speed) matters.
You start on a beach. You go to the moon. You come back. You go to Hollywood. You then go to the summit of Mount Everest. Have you
increased your gravitational potential energy more than if you had climbed to this summit without all the other side trips? No, the increase in
energy is the same. In both cases, the increase in gravitational potential energy equals your mass times the height of Mount Everest times g.
You are holding a cup of coffee at your desk, a half-meter above the floor. You extend your arm laterally out a nearby third-story window so
that the cup is suspended 10 meters above the ground. Have you increased the cup’s gravitational potential energy? No. Assume you choose
the floor as the zero potential energy point. The potential energy is the same because the cup remains the same distance above the floor.
An apple falls to the ground.Because the Earth’s gravity did work on it, the apple’s energy has increased. It depends on how you define “the
system.” If you said the apple had gravitational potential energy, then you are including the Earth as part of the system. In this case, the Earth’s
gravity is not an external force. Energy is conserved: The system’s decreased PE is matched by an increase in KE. You could also say “the
system” is solely the apple. In that case, it has no PE, since PErequires the presence of a force between objects in a system, and this system
has only one object. Gravity is now an external force acting on the apple, and it does increase the apple’s KE. This is not, perhaps, the typical
way to think about it, but it is valid.It is impossible for a system to have negative PE. Wrong: Systems can have negative PE. For instance, if you define the system to have zero
PE when an object is at the Earth’s surface, the object has negative PE when it is below the surface. Its PE has decreased from zero, so it
must be negative. Negative PE is common in some topics, such as orbital motion.(^140) Copyright 2007 Kinetic Books Co. Chapter 06