two forces F1 and F2 with magnitudes 6 lb and 10 lb, respectively, act on an object at a point P as shown in the figure. (Give your answers correct to one decimal place.)

Question

a) find the resultant force F acting on P

 i +  j

b)find the magnitude of F and its direction

|F|=

𝜃 =

Answer 1

Here's how to go about this question:

Turn your forces F1 and F2 into horizontal and vertical components. Assume F1 is at angle θ₁ above the horizontal and F2 is at angle θ₂ above the horizontal. The horizontal components for F1 are x = F1cos(θ₁) and y = F1sin(θ₁). Please remember to use the correct signs (+ or -) depending on which direction the vector is in. Similarly, do this for F2.

After you've done this, add the horizontal components of both forces to get the horizontal component of the resultant force. Also do this to the vertical components to get the vertical component of the resultant force. This will answer part A.

Find the magnitude by square rooting the sum of the squares of the components. Compute the angle by creating a triangle between the components and using the tan function.

I hope this helps!