Interesting Links (example problems):

A teflon box slides and eventually stops

Is mechanical energy conserved for a skier?

Wanna get stopped by a Mounty?

Serway shows you why...the completely general definition for work is:

You may recall that the dot product of two vectors is defined as:

Consider a body constrained to move in the x-direction. Suppose a force acts on it at some angle from the x-direction. The work equation would then become:

If the force and the angle are not functions of x, they can be taken outside the integral; the integral of dx is just x and, applying the limits...

This is the equation we were using in the first mini-lecture.

Spring Systems:

Systems containing springs are important because most physical systems can be modeled using springs of various force constants. To stretch a spring, a continuously increasing force must be applied: F = -kx.

Let's find the work required to stretch a spring an amount x:

For this reason, we define the (potential) energy U stored in a compressed or stretched spring as

Kinetic Energy:

Serway shows you, on page 153, that the work done by the net force (sigma F) is equal to the change in the kinetic energy of the system. This is called the work-energy theorem and you saw that this was so in Example 2 of the previous mini-lecture. It also suggests a definition for kinetic energy:

Graphical Presentations:

Figure 6.6, page 148, of Serway shows that the integral form for work was arrived at by summing the areas under the force vs position curve. In fact, the integral is the area under the curve!

Consider Figure 6.7 on page 149. The work done is the area, so

Example 1a: Work done by a varying force

Example 2: Two springs of different force constants; a graphical analysis

Example 3: Work done along a path

Example 4: Work done during a collision

Example 5: A two-block system and pulley done using energy methods instead of Newton's Laws

Example 6: Work done in compressing a spring