physHW1 - Physics 1111 Fall 2009 PS #1 Solutions Page 1 of...

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Unformatted text preview: Physics 1111 Fall 2009 PS #1 Solutions Page 1 of 7 Physics 1111 Problem Set #1 Solutions Problem 1: Choose which of the following equations are dimensionally consistent: v = at x = vt v 2 = 2 ax t = (2 x/a ) 1 / 2 t = a/v v = at 2 / 2 x = v/ 2 a “Dimensionally consistent” means, in this case, that the left-hand side and the right-hand side of an equation have the same dimensions. Dimensionless constants (like 2) don’t matter. Considering each of the equations above in turn: v = at = ⇒ [L] [T] = [L] [T] 2 [T] x = vt = ⇒ [L] = [L] [T] [T] v 2 = 2 ax = ⇒ [L] 2 [T] 2 = [L] [T] 2 [L] t = (2 x/a ) 1 / 2 = ⇒ [T] = parenleftBigg [L] [L] / [T] 2 parenrightBigg 1 / 2 = parenleftBigg [L][T] 2 [L] parenrightBigg 1 / 2 t = a/v = ⇒ [T] = [L] / [T] 2 [L] / [T] = [L][T] [L][T] 2 v = at 2 / 2 = ⇒ [L] [T] = [L] [T] 2 [T] 2 x = v/ 2 a = ⇒ [L] = [L] / [T] [L] / [T] 2 It should be fairly straightforward to see that the first four of these equations are dimen- sionally consistent, and the last three are not. Problem 2: How many significant figures does each of the following numbers have:. . . This question is designed to remind you of the rules for counting significant digits. Basically, the rules can be summed up as, “leading zeros don’t count; trailing zeros do.” So for example, a number like 0 . 0056 has two sig figs (the last two digits), whereas a number like 32 . 80 has four sig figs (that last zero has meaning). A number such as 120 may look somewhat ambiguous; does that zero mean this number has three significant digits, or just two? The convention is to say that this number has three sig figs. If we mean to write a number that specifies “around 120, but possibly a few more or less,” we should use scientific notation and write 1 . 2 × 10 2 , to make explicit that we only intend there to be two sig figs. Physics 1111 Fall 2009 PS #1 Solutions Page 2 of 7 Problem 3: Calculate the results of the following operations, round off to the correct number of significant digits, and enter your answers in scientific notation. (a) What is ( 1 . 03 )( 277 . 2 ) ? (b) What is 4 . 23 × 10- 7- 6 . 45 × 10- 9 ? (c) What is 53 . 5 + 119 . 7 ? (d) What is 2 π- 3 . 67 ? (a) For multiplication (or division), our answer should be quoted to the least number of sig figs of any of the multiplicands: (1 . 03)(277 . 2) = 285 . 516 . = 286 . (b) The rule for addition and subtraction is that we keep only as many decimal places ( not sig figs) as the smallest number in any of the terms. For this rule to work for numbers in scientific notation, they should all have the same power of ten: 4 . 23 × 10- 7- 6 . 45 × 10- 9 = 4 . 23 × 10- 7- . 0645 × 10- 7 = 4 . 1655 × 10- 7 ....
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This note was uploaded on 11/17/2009 for the course PHYS 1111 taught by Professor Plascak during the Spring '08 term at UGA.

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physHW1 - Physics 1111 Fall 2009 PS #1 Solutions Page 1 of...

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