Question

The y-component of the force F which a person exerts on the handle of the box wrench is known to be 86 lb. Determine the x-component and the magnitude of F.

Answer 1

Answer:

x-component of force is  38.18 lb where as magnitude of Force is 93.16

Explanation:

Fy of the force F exerted on the handle of the box wrench = 86 lb

Considering the triangle in Fig 1

magnitude of perpendicular = P =  12

magnitude of base = B = 5

using Pythagoras theorem

                        $H= \sqrt{P^{2} + B^{2}}$

                 $H= \sqrt{12^{2} + 5^{2}}$

            $H=13\\\implies cos \theta = \frac{5}{13} \\\implies sin \theta = \frac{12}{13}$

y-component of force is given given as:

                              $86 = Fsin\theta\\F = 86 (\frac{13}{12})\\F = 93.16 lb\\F_{x} =F cos \theta\\F_{x} = 93.16 (\frac{5}{13})\\F_{x} =38.18 lb.$