An object act upon by two forces 5N and 12N. calculate the resultant Of the two forces if the two forces act perpendicular to each other, if the two forces act at angle 40 degree to each other, if the two forces act at an angle 125 degree to each other

5 in x direction, 12 in y direction

hypotenuse = sqrt (25 +144) = 13 N
angle above x axis = tan^-1(12/5)

5 in x dir and 12 at 40 deg up
x component = 5 + 12 cos 40 = 14.2
y component = 12 sin 40 = 7.71
hypotenuse = sqrt ( 14.2^2 + 7.71^2)
angle above x axis = tan^-1 (7.71/14.2)

last one the same way

a. Fr = 5 + 12i = 13N.[67.4o]. = Resultant force.

b. Fr = 5 + 12[40o].
Fr = (5+12*cos40) + (12*sin40)I = 14.2 + 7.71i = 16.2N.[28.5o].

c. Fr = 5 + 12[125o].
Fr = (5+12*cos125) + (12*sin125)I
Fr = -1.88 + 9.83i =

Thank u

Thanx

12n-5n=7n

An object is acted upon by two forces 5N and 12N. Calculate the resultant of the two forces if the forces act perpendicular to each other.

Cosine rule:a²=b²+c²-2bc cos A
r=360-(40+40)
r=360°-80
r=280°/2=140°
Using the cosine rule:
R²=Z²+Y²-(2ZY) cos r
R²=5²+12²-(2*5*12) cos140°
R²=25+144-120*(-0.7660)
R²=169+91.92
R²=260.92
R=√260.92
R=16.1530
Using the sine rule
Sine z/5=sine140/16.1530
Sine z/5=0.6427/16
1530
Cross multiply
16.1630sin z=5*0.6427
Divide both sides by the coefficient of sin z
Sin z=0.1989
Z=sine^_1 0.1989
Z=sine^-1 0.1989
Z=11.5

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