Suppose the sand in a sand box with length 14 feet, width 8 feet, and height 1.5 feet is to be removed. The density of the sand (in pounds per cubic feet) h feet from the bottom is given by δ(h)=2.5−h. Find the work required to completely empty the sandbox.

The work required is  

Explanation:

  The volume of the sand box is mathematical represented as

Substituting 14 feet for L,  8 feet for W into the equation

The force as a result of the sand in the disk is mathematically represented as

     Substituting (2.5-h)  for

Now the work that is required to lift the sand from h = 0 to a height of  h=1.5 m is mathematically represented as

Now above is the formula for change in work done in order to obtain the workdone we integrate

! 55 !  

write a paragraph or story to explain the transformation between potential and kinetic energy as shown in your picture or model.  

you should have at least 5 complete sentences with a main idea and supporting details.  

you must include the following words:  

potential energy

kinetic energy

mechanical energy

conservation of energy

dude, this is hard lol : ))

potential energy is directly proportional to height.

more height = more potential energy.

greatest increase in height = greatest increase in potential energy

where are the points with the greatest increase in height ?

has to be c-e or d-e .