6.19 - Interactive problem: conservation of energy
The law of conservation of energy states that the total energy in an isolated system
remains constant. In the simulation on the right, you can use this law and your
knowledge of potential and kinetic energies to help a soapbox derby car make a
jump.
A soapbox derby car has no engine. It gains speed as it rolls down a hill. You can
drag the car to any point on the hill. A gauge will display the car’s height above the
ground. Release the mouse button and the car will fly down the hill.
In this interactive, if the car is traveling 12.5 m/s at the bottom of the ramp, it will
successfully make the jump through the hoop. Too slow and it will fall short; too fast
and it will overshoot.
You can use the law of conservation of energy to figure out the vertical position
needed for the car to nail the jump.
6.20 - Friction and conservation of energy
In this section, we show how two principles we have discussed can be combined to
solve a typical problem. We will use the principle of conservation of energy and how
work done by an external force affects the total energy of a system to determine the
effect of friction on a block sliding down a plane.
Suppose the 1.00 kg block shown to the right slides down an inclined wooden plane.
Since the block is released from rest, it has no initial velocity. It loses 2.00 meters in
height as it slides, and it slides 6.00 meters along the surface of the inclined plane. The
force of kinetic friction is 2.00 N. You want to know the block’s speed when it reaches
the bottom position.
To solve this problem, we start by applying the principle of conservation of energy. The
block’s initial energy is all potential, equal to the product of its mass, g and its height
(mgh). At a height of 2.00 meters, the block’s PE equals 19.6 J. The potential energy
will be zero when the block reaches the bottom of the plane. Ignoring friction, the PE of
the block at the top equals its KE at the bottom.
Now we will factor in friction. The force of friction opposes the block’s motion down the
inclined plane. The work it does is negative, and that work reduces the energy of the
block. We calculate the work done by friction on the block as the force of friction times
the displacement along the plane, which equals í12.0 J. The block’s energy at the top
(19.6 J) plus the í12.0 J means the block has 7.6 J of kinetic energy at the bottom.
Using the definition of kinetic energy, we can conclude that the 1.00 kg block is moving
at 3.90 m/s.
You can also calculate the effect of friction by determining how fast the block would be
traveling if there were no friction. All 19.6 J ofPEwould convert to KE, yielding a
speed of 6.26 m/s. Friction reduces the speed of the block by approximately 38%.
In general, non-conservative forces like friction and air resistance are dissipative forces:
They reduce the energy of a system. They do negative work since they act opposite the
direction of motion. (There are a few cases where they do positive work, such as when
the force of friction causes something to move, as when you step on a moving
sidewalk.)
Effect of non-conservative forces
Reduce object’s energy