Question

8. Two forces of 268 pounds and 487 pounds act at the origin and make angles of 34° and 68°, respectively,

with the positive x-axis. Find the resultant force. Round answer to 2 decimal places.

Answer 1

• The resultant force is 724.84 pounds with an angle of 55.94º with respect ot the x-axis.

Step-by-step explanation:

1. Write each force in terms of its components

a) F₁ = 268 pounds, 34° with the x-axis

`F_1=268* cos(34\°)\hat i+268* sin(34\°)\hat j`

`F_1=222.18\hat i+149.86\hat j`

b) F₂ = 487 pound, 68° with the x-axis

`F_2=487* cos(68\°)\hat i+487* sin(68\°)\hat j`

`F_2=182.43\hat i+451.54\hat j`

2. Add the corresponding components

`F_R=F_1+F_2=404.61\hat i+601.40\hat j`

The magntitude of the resultant force is:

`|F_R|=√((406.61)^2+(601.40)^2)=724.84` pounds

The angle is:

• arctan(601.40 / 406.1) = arctan(1.47906) = 55.94º.