Question

2.2 MODIFIED Two forces are applied as shown to a bracket support 670 lb a) Determine the magnitude and direction of the resultant force using the triangle rule Show that a second triangle (forces in a different order) will yield the same result. 60° b) 25° 500 lb

Answer 1

a)

$\underset{A}{\rightarrow}$ = - (500 Cos25) i + (500 Sin25) j = - 453.2 i + 211.3 j

$\underset{B}{\rightarrow}$ = (670 Cos60) i + (670 Sin60) j = 335 i + 580.23 j

$\underset{R}{\rightarrow}$ = ?

using triangle law

$\underset{R}{\rightarrow}$ = $\underset{A}{\rightarrow}$ + $\underset{B}{\rightarrow}$

$\underset{R}{\rightarrow}$ = (- 453.2 i + 211.3 j) + (335 i + 580.23 j )

$\underset{R}{\rightarrow}$ = - 118.2 i + 791.5 j

magnitude of resultant using pythagorean theorem is given as

| $\underset{R}{\rightarrow}$ | = sqrt((- 118.2)² + (791.5)²) = 800.3 lb

$\theta$ = 180 - tan^-1(791.5/118.2) = 98.5 deg

b)

$\underset{A}{\rightarrow}$ = - (500 Cos25) i + (500 Sin25) j = - 453.2 i + 211.3 j

$\underset{B}{\rightarrow}$ = (670 Cos60) i + (670 Sin60) j = 335 i + 580.23 j

$\underset{R}{\rightarrow}$ = ?

using triangle law

$\underset{R}{\rightarrow}$ = $\underset{B}{\rightarrow}$ + $\underset{A}{\rightarrow}$

$\underset{R}{\rightarrow}$ =  335 i + 580.23 j + - 453.2 i + 211.3 j

$\underset{R}{\rightarrow}$ = - 118.2 i + 791.5 j

magnitude of resultant using pythagorean theorem is given as

| $\underset{R}{\rightarrow}$ | = sqrt((- 118.2)² + (791.5)²) = 800.3 lb

$\theta$ = 180 - tan^-1(791.5/118.2) = 98.5 deg