
For example, in Newton's apocryphal story of the apple falling from a tree, the apple might be thought of as gaining energy because it goes from stationary (i.e. hanging motionless on a tree) to moving (i.e. falling rapidly towards Newton's head). The apple appears to have gained energy of motion (or kinetic energy). But according to the Newtonian view, the apple has not gained energy. Rather, the apple had energy all along  gravitational potential energy. The apple is not creating energy out of nothing as it's speed (and kinetic energy) increase. Instead, the apple's potential energy is being converted into kinetic energy.
The mechanism for this energy exchange is the physical idea of work. What is causing the apple to fall, thereby gaining speed (and kinetic energy), while it loses height (and potential energy)? Newton's answer was the force of gravity. Gravity is "doing work" on the apple by exerting a force.
The falling apple illustrates a situation in which the force doing work acts in the same direction as the direction of motion. However, a force might be exerted in a different direction from the direction of motion, as, for example, when a tow truck tows a disabled car see left figure below). Symbolically (right figure below), the amount of work done when a force causes an object to be displaced by a direction vector is the dot product of the two vectors:
Photo Credit: James Marshall, from a trip to Yosemite National Park, 1998 
Suppose that an object moves around the path in the direction shown. Your worksheet has been set up to calculate the work done by along each straight line segment of the path individually, and then to evaluate the total work done by when it acts on an object all of the way around . How is the total amount of work related to the amount of work done by along the straight line segments?
Do the results fit with your conjecture? Explain.



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