Calculus II - Applications to Physics and Engineering



Calculus II - Applications to Physics and Engineering

Work

When a constant force F moves an object through a distance d, the product W = Fd is defined as the work done by the force on that object. For example, in lifting a 3-lb textbook 2 feet you do an amount of work equal to W = 2ft x 3lb = 6ft/lb.

The work done by a variable force in moving an object along a line from location x = a to location x = b is found by integrating the force function from x = a to x = b

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Example: When a particle is located at a distance of x feet from the origin, a force of [pic]pounds acts on it. How much work is done in moving it from x=1 to x=3.

Example: A principle from elementary physics known as Hooke’s Law states that the force required to stretch or compress a spring a distance of x units from its natural length is proportional to that distance; that is

F(x) = kx, where k is known as the spring constant, which depends on the particular spring

1. A spring has spring constant k = 20lb/ft. The work done is stretching the spring 6 inches beyond its natural length is found by

2. The work done in stretching the spring in part a from 3 inches beyond its natural length to 6 in beyond its natural length is

3. A force of 40 N is required to hold a spring that has been stretched from its natural length of 10cm to 15 cm. How much work is doe in stretching the spring from 15cm to 18cm?

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