m/Discussion question C.
n/A hydraulic jack.
o/The surfaces are friction-
less. The black blocks are in
equilibrium.
The seesaw example demonstrates the principle of the lever,
which is one of the basic mechanical building blocks known as sim-
ple machines. As discussed in more detail in chapters 3 and 4, the
principle applies even when the interactions involved aren’t gravita-
tional.
Note that although a lever makes it easier to lift a heavy weight,
it also decreases the distance traveled by the load. By reversing the
lever, we can make the load travel a greater distance, at the expense
of increasing the amount of force required. The human muscular-
skeletal system uses reversed levers of this kind, which allows us to
move more rapidly, and also makes our bodies more compact, at the
expense of brute strength. A piano uses reversed levers so that a
small amount of motion of the key produces a longer swing of the
hammer. Another interesting example is the hydraulic jack shown
in figure n. The analysis in terms of gravitational energy is exactly
the same as for the seesaw, except that the relationship between ∆y 1
and ∆y 2 is now determined not by geometry but by conservation
of mass: since water is highly incompressible, conservation of mass
is approximately the same as a requirement of constant volume,
which can only be satisfied if the distance traveled by each piston is
in inverse proportion to its cross-sectional area.
Discussion Questions
A Hydroelectric power (water flowing over a dam to spin turbines)
appears to be completely free. Does this violate conservation of energy?
If not, then what is the ultimate source of the electrical energy produced
by a hydroelectric plant?
B You throw a steel ball up in the air. How can you prove based on
conservation of energy that it has the same speed when it falls back into
your hand? What if you threw a feather up? Is energy not conserved in
this case?
C Figure m shows a pendulum that is released at A and caught by a
peg as it passes through the vertical, B. To what height will the bob rise
on the right?
D What is wrong with the following definitions ofg?
(a) “gis gravity.”
(b) “gis the speed of a falling object.”
(c) “gis how hard gravity pulls on things.”2.1.6 Equilibrium and stability
The seesaw in figure k is in equilibrium, meaning that if it starts
out being at rest, it will stay put. This is known as a neutral equi-
librium, since the seesaw has no preferred position to which it will
return if we disturb it. If we move it to a different position and
release it, it will stay at rest there as well. If we put it in motion, it
will simply continue in motion until one person’s feet hit the ground.
Most objects around you are in stable equilibria, like the black86 Chapter 2 Conservation of Energy