What is work? If you hold a book out at arm's length for an hour without moving it, is that work? We have to be careful defining terms, since contradictions can arise.

Definition: The work done by a force F is given by

We'll deal with the dot product later (it's one of three kinds of multiplication in vector algebra). The above definition is valid if the force is constant; if it isn't, an integral (calculus) has to be used.
 

Example 1: The 15 kg block moves 5 m on a rough surface (µ_k = 0.129) under the influence of a 35 N force at 20 degrees from the horizontal. Draw a free body diagram. Find the normal and frictional forces, and the work done by each force on the free body.

Example 2: The 15 kg body is raised 5 m at constant speed by the force F. Find F. Also find the work done by the force F and the weight W during this process. If the force is removed and the body falls 5 m, what work would the weight do? What is the potential energy of the body at the 5 m position relative to its original position?

Definition: Potential energy equals the work necessary to raise the body to the height. Alternatively, it's the work done by the weight as the body falls through the same height.

Definition: Kinetic energy is defined as .
Work-energy theorem: The work done by the net force equals the change in the kinetic energy.

Example 4: Consider the loop-the-loop, which consists of a curved track attached to a circular loop. How high must we start the ball so that it goes completely around? When we try it experimentally, why must we start the ball higher? (Friction is not the only reason, but you may not be able to answer this question until you cover rotational energy.)