Today we covered basic examples of volumes (Sec 6.2) and work (Sec. 6.4). Here is the scan: wk3day7_wp.
The discussion on general area bounded by 2 curves on Tuesday paved the way to find the volume of a general class of object: solid of revolutions. We exploited the idea of Riemann sum again and sliced an arbitrary object into thin pieces, like a piece of bread from a loaf.
We then interpreted volume as a sum of these pieces, each approximated by the cross-sectional area times the width \(\triangle x\).
The same idea can be applied to physical problems as well. Like what we have done before for velocity and displacement, we investigated how work done of moving an object could be understood as a sum of the “pieces” too. Each piece is approximated by the formula \( W = F d \) and the infinite sum gives a natural definition of work when F may change with d (possibly linear or nonlinear way) as a whole.
A typed version of the word problems for work done (the explanation of the last question is expanded) is here: wordprob3_lecture7_withsol.