Question

Two people are carrying a box. One person exerts a force of 138 pounds at an angle of 49.2° with the horizontal. The other person exerts a force of 93 pounds at an angle of 59.5°. Find the weight of the box.

Answer 1

ANSWER:

230.1 pounds

STEP-BY-STEP EXPLANATION:

Given:

F1 = 138 pounds

θ1 = 49.2°

F2 = 93 pounds

θ2 = 59.5°

We can better understand the situation by the following sketch:

The vector for 138 pounds at 49.2 is:

$\begin{gathered} x=138\cdot\cos49.2\degree=90.17 \\ y=138\cdot\sin49.2\degree=104.47 \end{gathered}$

The vector for 93 pounds at 59.5 is

$\begin{gathered} x=93\cdot\cos59.5\degree=47.2 \\ y=93\cdot\sin59.5\degree=80.13 \end{gathered}$

Now, if we add the two vectors to obtain the resulting vector (i.e. the weight):

$\begin{gathered} W=(90.17+47.2,104.47+80.13) \\ W=(137.37,184.6) \end{gathered}$

Now, we calculate the normal of this vector W, just like this:

$\begin{gathered} ||W||=\sqrt{137.37^2+184.6^2} \\ ||W||=230.1\text{ pounds} \end{gathered}$

Box weight is 230.1 pounds