Question-52752

Question Number 52752 by afachri last updated on 12/Jan/19

Commented by afachri last updated on 12/Jan/19

Dear Sir, i′m just wondering is there a unique solution for F_2 and 𝛂 if : the resultant of F_1 and F_2 has to be 900 N (also vertical) when F_1 is 500 N. i just want to hear your opion Sir. Please don′t give me the solution first. in my opinion this question has no a unique solution. what do you say, Sir ??? Please

$$\boldsymbol{\mathrm{Dear}}\:\boldsymbol{\mathrm{Sir}},\: \\ $$$$\boldsymbol{\mathrm{i}}'\boldsymbol{\mathrm{m}}\:\boldsymbol{\mathrm{just}}\:\boldsymbol{\mathrm{wondering}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{there}}\:\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{unique}}\:\boldsymbol{\mathrm{solution}} \\ $$$$\boldsymbol{\mathrm{for}}\:\boldsymbol{\mathrm{F}}_{\mathrm{2}} \:\boldsymbol{\mathrm{and}}\:\boldsymbol{\alpha}\:\boldsymbol{\mathrm{if}}\::\:\boldsymbol{{the}}\:\boldsymbol{{resultant}}\:\boldsymbol{{of}}\:\boldsymbol{\mathrm{F}}_{\mathrm{1}} \:\boldsymbol{\mathrm{and}} \\ $$$$\boldsymbol{\mathrm{F}}_{\mathrm{2}} \:\boldsymbol{\mathrm{has}}\:\boldsymbol{\mathrm{to}}\:\boldsymbol{\mathrm{be}}\:\mathrm{900}\:\mathrm{N}\:\left(\boldsymbol{\mathrm{also}}\:\boldsymbol{\mathrm{vertical}}\right)\:\boldsymbol{\mathrm{when}}\:\boldsymbol{\mathrm{F}}_{\mathrm{1}} \\ $$$$\boldsymbol{\mathrm{is}}\:\mathrm{500}\:\boldsymbol{\mathrm{N}}. \\ $$$$\boldsymbol{\mathrm{i}}\:\boldsymbol{\mathrm{just}}\:\boldsymbol{\mathrm{want}}\:\boldsymbol{\mathrm{to}}\:\boldsymbol{\mathrm{hear}}\:\boldsymbol{\mathrm{your}}\:\boldsymbol{\mathrm{opion}}\:\boldsymbol{\mathrm{Sir}}.\:\boldsymbol{\mathrm{Please}} \\ $$$$\boldsymbol{\mathrm{don}}'\boldsymbol{\mathrm{t}}\:\boldsymbol{\mathrm{give}}\:\boldsymbol{\mathrm{me}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{solution}}\:\boldsymbol{\mathrm{first}}.\:\boldsymbol{\mathrm{in}}\:\boldsymbol{\mathrm{my}}\:\boldsymbol{\mathrm{opinion}} \\ $$$$\boldsymbol{\mathrm{this}}\:\boldsymbol{\mathrm{question}}\:\boldsymbol{\mathrm{has}}\:\boldsymbol{\mathrm{no}}\:\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{unique}}\:\boldsymbol{\mathrm{solution}}. \\ $$$$\boldsymbol{\mathrm{what}}\:\boldsymbol{\mathrm{do}}\:\boldsymbol{\mathrm{you}}\:\boldsymbol{\mathrm{say}},\:\boldsymbol{\mathrm{Sir}}\:???\:\boldsymbol{\mathrm{Please}} \\ $$

Commented by mr W last updated on 12/Jan/19

if the resultant of F_1 and F_2 is given, in size (900 N) and in direction (vertical), then there must be an unique F_2 , both in size and in direction. F_1 ^→ +F_2 ^→ =R^→ ⇒F_2 ^→ =R^→ −F_1 ^→ , this is unique.

$${if}\:{the}\:{resultant}\:{of}\:{F}_{\mathrm{1}} \:{and}\:{F}_{\mathrm{2}} \:{is}\:{given}, \\ $$$${in}\:{size}\:\left(\mathrm{900}\:{N}\right)\:{and}\:{in}\:{direction}\:\left({vertical}\right), \\ $$$${then}\:{there}\:{must}\:{be}\:{an}\:{unique}\:{F}_{\mathrm{2}} ,\:{both} \\ $$$${in}\:{size}\:{and}\:{in}\:{direction}. \\ $$$$\overset{\rightarrow} {{F}}_{\mathrm{1}} +\overset{\rightarrow} {{F}}_{\mathrm{2}} =\overset{\rightarrow} {{R}} \\ $$$$\Rightarrow\overset{\rightarrow} {{F}}_{\mathrm{2}} =\overset{\rightarrow} {{R}}−\overset{\rightarrow} {{F}}_{\mathrm{1}} ,\:{this}\:{is}\:{unique}. \\ $$

Commented by afachri last updated on 12/Jan/19

oh thank you Mr W for your opinion. i understand it. i′ll start to calculate and determine their values. Thank You very much, Mr W.

$$\mathrm{oh}\:\mathrm{thank}\:\mathrm{you}\:\mathrm{Mr}\:\mathrm{W}\:\mathrm{for}\:\mathrm{your}\:\mathrm{opinion}. \\ $$$$\mathrm{i}\:\mathrm{understand}\:\mathrm{it}.\:\mathrm{i}'\mathrm{ll}\:\mathrm{start}\:\mathrm{to}\:\mathrm{calculate}\:\mathrm{and} \\ $$$$\mathrm{determine}\:\mathrm{their}\:\mathrm{values}. \\ $$$$\mathrm{Thank}\:\mathrm{You}\:\mathrm{very}\:\mathrm{much},\:\mathrm{Mr}\:\mathrm{W}. \\ $$$$ \\ $$

Commented by peter frank last updated on 12/Jan/19

$${please}\:{check}\:{QN}\:\:\mathrm{52708} \\ $$

Commented by mr W last updated on 12/Jan/19

$${sorry}\:{i}\:{can}'{t}\:{help}\:{you}\:{in}\:{that}\:{question}. \\ $$

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