Question Number 224753 by Tawa11 last updated on 01/Oct/25
Commented by fantastic last updated on 01/Oct/25
$${wdym}\:{by}\:{magnitude}\:{of}\:{reaction} \\ $$$${is}\:{the}\:{mass}\:{of}\:{the}\:{block}\:{on}\:{inclined} \\ $$$${surface}\:{is}\:\mathrm{7}{kg}? \\ $$
Commented by Ernestolisboa last updated on 07/Oct/25
Answered by mr W last updated on 02/Oct/25
Commented by mr W last updated on 02/Oct/25
$${R}_{{x}} =\mathrm{8}{g}\:\mathrm{sin}\:\mathrm{16}°−\mathrm{1}.\mathrm{6}{g}\:\mathrm{cos}\:\mathrm{37}° \\ $$$${R}_{{y}} =\mathrm{7}{g}+\mathrm{1}.\mathrm{6}{g}\:\mathrm{sin}\:\mathrm{37}°−\mathrm{8}{g}\:\mathrm{cos}\:\mathrm{16}° \\ $$$$\Rightarrow{R}=\sqrt{\left(\mathrm{8}{g}\:\mathrm{sin}\:\mathrm{16}°−\mathrm{1}.\mathrm{6}{g}\:\mathrm{cos}\:\mathrm{37}°\right)^{\mathrm{2}} +\left(\mathrm{7}{g}+\mathrm{1}.\mathrm{6}{g}\:\mathrm{sin}\:\mathrm{37}°−\mathrm{8}{g}\:\mathrm{cos}\:\mathrm{16}°\right)^{\mathrm{2}} } \\ $$$$\:\:\:\:\:\:\:\:\approx\mathrm{0}.\mathrm{966}{g}\approx\mathrm{9}.\mathrm{482}\:{N} \\ $$
Commented by Tawa11 last updated on 03/Oct/25
$$\mathrm{Thanks}\:\mathrm{sir}. \\ $$$$\mathrm{I}\:\mathrm{appreciate}. \\ $$
Commented by fantastic last updated on 03/Oct/25
$${do}\:{you}\:{know}\:{the}\:{ans}? \\ $$
Commented by Tawa11 last updated on 03/Oct/25
$$\mathrm{No} \\ $$
Commented by mr W last updated on 03/Oct/25
$${is}\:{it}\:{not}\:{easy}\:{to}\:{check}\:{what}\:{the} \\ $$$${right}\:{answer}\:{is}? \\ $$
Commented by mr W last updated on 03/Oct/25
$${to}\:{be}\:{honest},\:{i}'{m}\:{wondering}\:{that}\:{there} \\ $$$${is}\:{actually}\:{doubt}\:{about}\:{it}\:{to}\:{you}. \\ $$$${here}\:{the}\:{wished}\:{explanation}: \\ $$$${totally}\:\mathrm{4}\:{forces}\:{are}\:{acting}\:{on}\:{the} \\ $$$${object}\:{on}\:{the}\:{inclined}\:{surface}: \\ $$$${tension}\:{from}\:{upper}\:{string}:\:\mathrm{8}{g} \\ $$$${tension}\:{from}\:{lower}\:{string}:\:\mathrm{1}.\mathrm{6}{g} \\ $$$${self}−{weight}\:{of}\:{the}\:{object}:\:\mathrm{7}{g} \\ $$$${reaction}\:{force}\:{from}\:{the}\:{contact}\:{surface}:\:{R} \\ $$$$ \\ $$$${the}\:{reaction}\:{force}\:{R}\:{is}\:{the}\:{resultant} \\ $$$${from}\:{normal}\:{force}\:{N}\:{and}\:{friction} \\ $$$${force}\:{f}.\: \\ $$$$ \\ $$$${say}\:{the}\:{components}\:{of}\:{R}\:{in}\:{x}−\:{and} \\ $$$${y}−{directions}\:{are}\:{R}_{{x}} \:{and}\:{R}_{{y}} \:{respectively}. \\ $$$${since}\:{the}\:{object}\:{is}\:{in}\:{equilibrium}, \\ $$$${in}\:{the}\:{shown}\:{coordinate}\:{system}, \\ $$$${we}\:{have} \\ $$$$\Sigma{F}_{{x}} =\mathrm{0}\:\Rightarrow\:{R}_{{x}} −\mathrm{8}{g}\:\mathrm{sin}\:\mathrm{16}°+\mathrm{1}.\mathrm{6}{g}\:\mathrm{cos}\:\mathrm{37}°=\mathrm{0} \\ $$$$\Sigma{F}_{{y}} =\mathrm{0}\:\Rightarrow\:{R}_{{y}} −\mathrm{7}{g}−\mathrm{1}.\mathrm{6}{g}\:\mathrm{sin}\:\mathrm{37}°+\mathrm{8}{g}\:\mathrm{cos}\:\mathrm{16}°=\mathrm{0} \\ $$$${we}\:{get} \\ $$$${R}_{{x}} =\mathrm{8}{g}\:\mathrm{sin}\:\mathrm{16}°−\mathrm{1}.\mathrm{6}{g}\:\mathrm{cos}\:\mathrm{37}° \\ $$$${R}_{{y}} =\mathrm{7}{g}+\mathrm{1}.\mathrm{6}{g}\:\mathrm{sin}\:\mathrm{37}°−\mathrm{8}{g}\:\mathrm{cos}\:\mathrm{16}° \\ $$$${and}\:{R}=\sqrt{{R}_{{x}} ^{\mathrm{2}} +{R}_{{y}} ^{\mathrm{2}} } \\ $$$$ \\ $$$${certainly}\:{we}\:{can}\:{also},\:{but}\:{not}\:{must}, \\ $$$${take}\:{a}\:{rotated}\:{coordinate}\:{system}\: \\ $$$${as}\:{you}\:{did}.\:{but}\:{i}\:{think}\:{it}'{s}\:{better}\:{to} \\ $$$${do}\:{as}\:{i}\:{did},\:{because}\:{the}\:{question} \\ $$$${only}\:{asked}\:{for}\:{the}\:“{total}''\:{reaction} \\ $$$${force},\:{not}\:{the}\:{normal}\:{reaction}\:{N} \\ $$$${and}\:{the}\:{friction}\:{f}. \\ $$
Commented by fantastic last updated on 03/Oct/25
$${sir}\:{how}\:{is}\:{that}\:\mathrm{16}^{\mathrm{0}} \\ $$
Commented by mr W last updated on 03/Oct/25
Commented by fantastic last updated on 03/Oct/25
$${sir}\:{i}\:{genuinely}\:{request}\:{you} \\ $$$${to}\:{explain}\:{the}\:{answer}. \\ $$$${to}\:{be}\:{honest}\:{i}\:{actually}\:{do} \\ $$$${not}\:{understand}\:{the}\:{question} \\ $$$${completly} \\ $$
Commented by fantastic last updated on 04/Oct/25
$${thank}\:{you}\:{very}\:{much}\:{sir}. \\ $$$${God}\:{bless}\:{you} \\ $$