hw01soln - Phys ic s 1 4 4 Va is hna v S pr ing 2 0 1 0 Ho...

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Phys ic s 1 4 4 – Vais hnav Spring 2 0 1 0 Ho w Thing s Wo rk Home work Se t # 1 Solut ions Pro ble m 1 : a) Chapt e r 1 , Exe rc is e 2 ( p. 3 8 ) : As y o u jump ac ro s s a s mall s t re am, do e s a ho rizo nt al fo rc e ke e p y o u mo ving fo rward? What is t hat fo rc e ? No—once you ar e in the air , no for ce acts on you. You ar e car r ied for war d by iner tia. b) Chapt e r 1 , Exe rc is e 4 ( p. 3 8 ) : Why do e s t apping y o ur t o o t hbrus h o n t he s ink dry it o ff? Water is slipper y and is not held to the toothbr ush by much fr iction. When the toothbr ush stops, ver y little for ce acts on the water , which keeps moving for war d due to iner tia. c ) Chapt e r 1 , Exe rc is e 6 ( p. 3 8 ) : An uns e at be lt e d drive r c an be injure d by t he s t e e ring whe e l during a he ad- o n c o llis io n. Why do e s t he drive r hit t he s t e e ring whe e l whe n t he c ar c o me s t o a s t o p? Befor e the cr ash, car , seat, and dr iver ar e all moving for war d. A for ce acts on the car and stops it. However if the dr iver is not wear ing a seat belt, he or she is not attached to the car , which then exer ts no dir ect for ce on the dr iver ’s upper body. So due to its iner tia, the dr iver ’s upper body keeps moving for war d, even when the car has stopped. Pro ble m 2 : As part o f Lab #1 , e ac h pe rs o n in t he c las s c o unt e d t he t o t al numbe r o f M&M’s in his o r he r o wn bag . The re we re 2 3 bag s c o unt e d, and t he individual re s ult s fo llo w: 5 6 , 5 6 , 5 8 , 6 0 , 5 7 , 5 9 , 5 7 , 5 5 , 5 9 , 5 9 , 5 5 , 5 8 , 5 8 , 5 9 , 6 0 , 6 1 , 5 8 , 5 8 , 5 8 , 5 7 , 5 7 , 6 0 , 5 9 . a) Calc ulat e t he e xpe rime nt al me an, t he s t andard de viat io n, and t he s t andard de viat io n o f t he me an. Yo u do n’t have t o s ho w all y o ur c alc ulat io ns he re , but y o u do ne e d t o e xplain ( wit h wo rds o r wit h e quat io ns ) ho w y o u c alc ulat e d e ac h o f t he re que s t e d quant it ie s . Sinc e we ’re t alking abo ut numbe rs o f M&M’s , ro und y o ur final ans we rs t o t he t e nt hs plac e ( i. e y o u wo uld ro und 2 . 4 1 3 t o 2 . 4 ) . Using the same techniques as in the lab, I calculated the exper imental mean by adding up all the values and then dividing by the total number ( in this case, 2 3 ) to obtain 5 8 . To calculate the standar d deviation, I took each of the individual values, subtr acted the exper imental mean fr om them, and took the aver age of those number s. Then, I took the squar e r oot of the aver age to obtain 1 .5 6 , which I r ounded to 1 .6 following the instr uctions. To get the standar d deviation of the mean, I took the standar d deviation and divided by the squar e r oot of the number of tr ials ( measur ements) to obtain 0 .3 3 , which I r ounded to 0 .3 . I summar ize the r esults in the table befor e.
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