APPLICATIONS OF INTEGRATION ANIMATIONS

APPLICATIONS OF INTEGRATION ANIMATIONS

Area under a curve using rectangles and a left approximation. Click on the picture on the left to see an animation.

Look at this animation (see picture on the left) and see if you can figure out how much work is done against gravity in lifting the chain and the weight attached to the end of it up to the ceiling. After the "oops" the weight comes loose and falls back to the floor. How fast is the weight traveling (neglecting air resistance) when it hits the floor?

A rectangular box shaped container of water has dimensions 10' by 2' by 10' (see picture below). It is filled with water to a depth of 4 feet (again see picture). Using a large tube the water is to be pumped out of the box. In doing so all the water will need to be pumped to a height that is 4 feet above the top of the box after which is will fall to the ground. Compute the total work done against gravity in pumping all the water to a height 4 feet above the top of the box. Click on either picture below to see an animation of what is happening.

Spring Stretching Example

A force of 100 pounds will stretch a spring 2 feet beyond its equilibrium length of 5 feet. Find the work done in stretching the spring from a length of 5 feet to a length of 8 feet. Click here to see an animation and click here to see an animation with scales.

100 = 2k so the spring constant is 50. The work done would be

How much additional work would be done in stretching the spring two more feet (assuming we are still within the elastic limits of the spring and Hooke's Law holds)?

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Lane Vosbury, Mathematics, Seminole State College email: vosburyl@seminolestate.edu