Three forces are applied to a gusset plate as shown in the figure below. Determi

Question

Three forces are applied to a gusset plate as shown in the figure below. Determine the following:

i. Magnitude of the resultant of these forces,

ii. Angle between the line of action of the resultant and the positive x-axis

iii. Write the resultant in Cartesian form.

Three forces are applied to a gusset plate as shown in the figure below. Determine the following: Magnitude of the resultant of these forces, Angle between the line of action of the resultant and the positive x-axis Write the resultant in Cartesian form.

Explanation / Answer

the 300 N force is 300cos(45) i + 300sin(45) j

the 250 N force is 250cos(90+40) i + 250 sin(90+40) j

the angle of the third vector is 37 degrees to the negative x axis

so 425 N force = 425cos(90+53) i + sin(90+53)j

so the resultant force is the sum of all forces

(300cos(45) i + 300sin(45) j ) + ( 250cos(90+40) i + 250 sin(90+40) j) +(425cos(90+53) i + 425 sin(90+53)j)

= (-287.98 i + 659.41 j) ---------- caartesian form

magnitude is (sqrt (-287.98)^2 + (659.41)^2) = 715.99 N

angle is arc tan (659.41/-287.98) = 113.59 degrees

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