What is the cannonball’s velocity
at 125 m? Its mass is 3.20 kg.
W = ǻPE + ǻKE
W = mgǻh + ǻKE
12,500 J = (3.20 kg)(9.80 m/s^2 )(125 m)
+ǻKE
ǻKE = 8,580 J
½mv^2 = 8,580 J
v^2 = 2(8,580 J)/(3.20 kg)
v = 73.2 m/s
6.15 - Conservative and non-conservative forces
Earlier, when discussing potential energy, we mentioned that we would explain
conservative forces later. The concept of potential energy only applies to conservative
forces.
Gravity is an example of a conservative force. It is conservative because the total work
it does on an object that starts and finishes at the same point is zero. For example, if a
20 kg barbell is raised 2.0 meters, gravity does í40 J of work, and when the barbell is
lowered 2.0 meters back to its initial position, gravity does +40 J of work. When the
barbell is returned to its initial position, the sum of the work done by gravity on the
barbell equals zero.
You can confirm this by considering the barbell’s gravitational potential energy. Since
that equals mgh, it is the same at the beginning and end because the height is the
same. Since there is no change in gravitational PE, there is no work done by gravity on
the barbell.
We illustrate this with the roller coaster shown in Concept 1. For now, we ignore other
forces, such as friction, and consider gravity as the only force doing work on the roller
coaster car. When the roller coaster car goes down a hill, gravity does positive work.
When the roller coaster car goes up a hill, gravity does negative work. The sum of the
work done by gravity on this journey equals zero.
When a roller coaster car makes such a trip, the roller coaster car travels on what is
called a closed path, a trip that starts and stops at the same point. Given a slight push
at the top of the hill, the roller coaster would make endless trips around the roller
coaster track.
Kinetic friction and air resistance are two examples of non-conservative forces. These
forces oppose motion, whatever its direction. Friction and air resistance do negative
work on the roller coaster car, slowing it regardless of whether it is going uphill or
downhill.
We show non-conservative forces at work in Concept 2. The roller coaster glides down
the hill, but it does not return to its initial position because kinetic friction and air
resistance dissipate some of its energy as it goes around the track. The presence of
these forces dictates that net work must be done on the roller coaster car by some other
force to return it to its initial position. A mechanism such as a motorized pulley system can accomplish this.
A way to differentiate between conservative and non-conservative forces is to ask: Does the amount of work done by the force depend on the
path?
Consider only the force of gravity, a conservative force, as it acts on the skier shown in Concept 3. When considering the work done by gravity,
it does not matter in terms of work and energy whether the skier goes down the longer, zigzag route (path A), or the straight route (path B). The
work done by gravity is the same along either path. All that matters are the locations of the initial and final points of the path. The conservative
Conservative force
A force that does no work on closed
pathNon-conservative force
A force that does work on closed path