All in a Good Day’s Work Calculus Honors Project by Brandon Sasser and Terra Pumphrey

What is work? Definition of Work Done by a Constant Force If an object is moved a distance D in the direction of an applied force F, then the work W done by the force is defined as W = F x D.

Example Lifting an Object Suppose an athlete wanted to lift a 250 lb barbell 3 ft off the ground. W = 250 lb(3 ft) = 750 ft-lbs

Work Done by a Variable Force If an object is moved along a straight line by a continuously varying force F(x), then the work W done by the force as the object is moved from x = a to x = b is represented by the following equations:

Pumping Water A cylindrical water tank 4 meters high with a radius of 2 meters is buried so that the top of the tank is 1 meter below ground level. How much work is done in pumping a full tank of water up to ground level if the water weighs 9800 newtons per cubic meter?

Solution

Working for a Drink On a hot afternoon in Panama City Beach, Terra is trying to cool off by sipping a glass of “palm wine.” How much work does she have to do to empty the glass? Initially, the glass is filled to a vertical depth of 8 cm.  The force due to gravity acting on 1 gram is 980 dynes, and in these units, work is measured in ergs.

Diagram 1 10 cm 15 cm 10 cm 8 cm

Diagram 2

Solution