phy1020.DVI
2.6 Unit Conversions It is very common to have to work with quantities that are given in units other than the units you’d like t ...
Finally, do the arithmetic: 60 mile hr 5280 ft 1 mile 1 hr 3600 sec D 88 ft sec (2.12) Example.Convert250;000furlongs per fo ...
Each country has its own currency units. Examples are United States dollars ($), British pounds sterling (£), European euros (e ...
Chapter 3 Problem-Solving Strategies Much of this course will focus on developing your ability to solve physics problems. If you ...
Check your answer for reasonableness—don’t just write down whatever your calculator says. For example, suppose you’re computing ...
Chapter 4 The Calculus Some ideas in physics are most naturally expressed in terms of a branch of mathematics calledthe calculus ...
Division of infinitesimals leads to some interesting results. In general, dividing one infinitesimal number by another often lea ...
Cancelingxin the numerator and denominator, slopeD lim x! 0 2xCx (4.15) and asxapproaches zero, slopeD2x (4.16) So for at an ...
These results will be proved in a more rigorous calculus course. Now we know how to find the slope of a line that is non necessa ...
Figure 4.1: Finding the area under a curve using rectangles (Credit: pleacher.com) To do this, imagine dividing the area under t ...
It is important to note that the area under the curve counts asnegativearea if it lies below thexaxis. For example, consider a s ...
constant): Z audxDa Z udx (4.46) Z .uCv/dxD Z udxC Z vdx (4.47) Z .uv/dxD Z udx Z vdx (4.48) These results will be proved in a ...
Notice that the constant of integrationCalways cancels out in a definite integral. 4.4 The Fundamental Theorem of Calculus Thefu ...
the integral as the sum of the rectangle areas. For example, for the body we’ve been using for our example, how far does the bod ...
to be ZR 0 p R^2 x^2 dxD 1 2 x p R^2 x^2 CR^2 tan^1 x p R^2 x^2 ˇˇ ˇ ˇ ˇ R 0 (4.70) D 1 2 2 R^2 0 D 4 R^2 (4. ...
where in the last step we movedR^2 =2outside the integral because it’s a constant. Now evaluate theintegral: Z2 0 ZR 0 rdrdD ...
and we have derived the classical formula. Fence Enclosing Maximum Area Let’s look at an optimization problem. Say you have a pe ...
Therefore, to maximize the play area for your dog, you should make one side (the side parallel to the side of the house) equal t ...
II Waves Waves ...
Chapter 5 Simple Harmonic Motion We begin our study of waves with the study ofsimple harmonic motion. Simple harmonic motion is ...
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