THE MIND & THE SCIENCE OF SUCCESS - All rights reserved - - APPENDIX -

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1 - APPENDIX - MAYARD S PROBLEM SOLVING METOD A sample o word problems rom hgh school (nd cycle) to college leel s used to llustrate ths smple method that can also be used n all grade leels. 4 smple steps U: Understand the problem and the queston to be resoled I: Identy the arables and the data proded n the queston. S : Start to sole wth what you know V : Very your answer Scence Grade 9 Brne s a soluton o sodum chlorde (NaCl) at % m/, whch s used to presere certan oods. To prepare 4 ml o brne, how much salt must be dssoled? Soluton:. U: Understand the problem and the queston We want to nd the mass o salt (M). I: Identy the arable and the data C = % (m/) ; V = 4ml ; M=? = g ml =. g/ml. S: start to sole wth what you know M C V C x V=M. x 4 = M g = M

2 4. Vercaton Does the calculated mass allow us to obtan the ntal concentraton? M g C,g / ml (yes) V 4ml

3 Scence & the enronment Grade ( multple steps) A welder puts a 5g bar o ron, heated to65 C, n 5ml o at C. The temperature rses to 5 C. Assumng no energy has been lost to the surroundngs, calculate the specc heat capacty o ron. Soluton.U: Understand the problem and the queston We want to nd the specc heat capacty o (Cron)..I: Identy the arable and the data T = T = Water C 5 C V = 5ml m=5g ( ml o =g) C = 4,9 J/g C Q=? T = T = 65 5 C C Iron m=5g Cron =? Qron = -Q (ron releases energy).s: start to sole wth what you know Remark: Startng wth what you know wll enable you to see the other steps that must be completed The thermal energy ormula or ron s : Q ron mct Q ron 5 c(5 65) Next step: nd Qron = -Q The thermal energy o s: Q Q mct (5 ) Q 9J Qron = -Q = -9 J

4 The specc heat capacty o ron s : Q er 5c(565) 9 5 c ( ) 9 c 5 ( ).45J / g C c 4. V: Vercaton Is the calculated specc heat capacty o ron (Cron =.45J / g C ) equal to the expermental alue C ron exp ermental.45j / g C (yes) 4

5 Chemstry Grade ydrogen cyande (CN) s a colorless gas that s extremely toxc because t preents the transportaton o tal oxygen to the body s cells and tssues. In ndustry, the hydrogen cyande s ormed rom the reacton o methane ( C 4 ) and ammona ( N ) accordng to the ollowng equaton: C N CN 4 ( ) ( g) ( g) g ( g) what s the rate o hydrogen ormaton the concentraton o ammona goes rom.5 mole /L to.5 mol /L n.75 mnutes..u: Understand the problem and the queston We want to nd the rate o hydrogen ormaton ( r )..I: Identy the arable and the data N.5mol / L ; N.5mol / L.S: start to sole wth what you know ; t =.75 mn = 5 s ; r? ; r? Remark: Startng wth what you know wll enable you to see the other steps that must be completed. The reacton rate ormula o hydrogen s: r r Next step: We nd r =? The general ormula o the reacton rate s : r r r C N CN t 4 t N N N ( ) t t (,5,5).56 5 t mol /( L s) t 5

6 Let s now nd the reacton rate o hydrogen: r r r r ( ) r mol /( L s) r TE MIND & TE SCIENCE OF SUCCESS 4. Vercaton By obserng the chemcal reacton, we notce that the reacton rate o hydrogen s tmes the one o hydrogen cyande; The reacton rate o hydrogen s: r r.56 CN mol /( L s) r r CN Is the reacton rate o hydrogen tmes the reacton rate o ydrogen cyande? r r CN (yes) 6

7 Physcs (mechancs) College (multple steps problem) A der standng on a dng board drops her nose clp rom a heght o 5 m rom the s surace. Water resstance slows the nose clp at a constant rate o 5 m / s. What depth wll the nose clp reach? Soluton. U : understand the problem and the queston to sole Problem: the stuaton noles knematcs concepts Queston to be resoled: We need to nd the depth o the nose clp n the. Drawng: to ncrease understandng, we draw a dagram o the stuaton. 7

8 . I : Identy the arables and the mportant data Medum Ar y 5m (ollowng the axs) m / s? a 9.8m / s a Medum 8m / s ( poste deceleraton ollowng the axs)? m/ s y?. S : start wth what you know Remark: Startng wth what you know wll enable you to see the other steps that must be completed. The depth o the nose clp ( y ) n the s: a y (8) y need to nd the ntal elocty The ntal elocty n the : n ar The nal elocty n ar s: a ar y ( 9.8)( 5) m / s ntal elocty n s : 7.5m / s Fnally, the depth o the nose clp ( y ) n the s: a y (7.5) (8) y 94.5 y 5. 5m 56 8

9 4.Vercaton Does a dsplacement o -5.5 metres n, correspond to an ntal elocty o 7.5 m/s? a y (8)( 5.5) m / s ( yes) 9