Question

Calculate the equilibrium force when the following forces are combined:

(1) 650 N at 74°,
(2) 1300 N at 278°,
(3) 570 N at 233°, and
(4) 500 N at 101°.

a. 1960 N at 174°
b. 1720 N at 238°
c. 2080 N at 124°
d. 1840 N at 306°

Answer 1

The equilibrium force when the following forces are combined is:

1720 N at 238°

How to calculate the equilibrium force?

The sum of the horizontal forces in the x-direction are:

`F_(x)` = (650 cos 74°) + (1300 cos 278°) + (570 cos 233°) + (500 cos 101°)

`F_(x)` = 179.16 + 180.93 - 343.03 - 95.4

`F_(x)` = -78.34

The sum of the vertical forces in the y-direction are:

`F_(y)` = (650 sin 74°) + (1300 sin 278°) + (570 sin 233°) + (500 sin 101°)

`F_(y)` = 624.82 - 1287.35 - 455.22 + 490.81

`F_(y)` = -626.94

Resolving this forces gives:

F = 1720 N at 238°