# 86 Comparing Work-Energy and Energy Conservation*

In the previous chapters we analyzed a person’s jump using the rather than the . Examining that correspondence between these concepts will allow us to learn a few important concepts. Let’s refresh ourselves with that example:

### Everyday Examples: Jumping

During a jump a person’s legs might apply a force of 1200 **N** upward on their while the center of mass moves 0.3 **m **upward. Let’s figure out what their launch and hang time will be if the person has a weight of 825 **N**.

First we calculate the done by their legs.

was acting on them during the launch phase as well, so we need to calculate the done by gravity:

The net work is then:

The tells us to set the change in equal to the . We will keep in mind that they started at rest, so the initial kinetic energy was zero.

We can see that we need the person’s mass. We just divide their weight by *g*= 9.8** m/s/s **to find it:

We isolate the final speed at the end of the launch phase (as the person leaves the ground) and insert the mass.

Then we take the square root the result to find the :

In the first part of the jumping example we calculated the on the object and used the to find the change in . In equation form it looks like this:

Moving the done by to the other side:

The looks like this:

Remembering that we ignored and , and that nothing was permanently deformed, .

Gravity did negative work because it points down and motion was upward, but the effect of that work was to increase potential energy by transferring some of the person’s into their own. Therefore change in gravitational potential energy should be the negative of the work done by gravity. This work was internal to the Earth-person system, so the only work being done on the person’s from the outside was work done by the legs. Making these replacements we have:

Which is exactly the we started with. We can either use the on a given object and include work done by resistance to and in the , and say all of that work contributes to changing kinetic energy, or instead use the and instead say that work done by elastic forces and gravity contributes to and instead of . Either way is equivalent, as we have just seen.

the change in kinetic energy of an object or system is equal to the net work done on the object or system

the net work on a system must be equal to the sum of the changes in kinetic, potential, and thermal energies

a point representing the mean (average) position of the matter in a body or system

distance traveled per unit time

A quantity representing the effect of applying a force to an object or system while it moves some distance.

energy which a body possesses by virtue of being in motion, energy stored by an object in motion

total work done on an object, equal to the addition of all separate works done on the object, or the work done by the net force

a force that acts on surfaces in opposition to sliding motion between the surfaces

a force acting opposite to the relative motion of any object moving with respect to a surrounding fluid

potential energy stored in objects based on their relative position within a gravitational field

a point at which the force of gravity on body or system (weight) may be considered to act. In uniform gravity it is the same as the center of mass.

reduction in size caused by application of compressive forces (opposing forces applied inward to the object).

energy stored in the deformation of a material