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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.

Respuesta :

Edufirst

Answer:

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

Explanation:

1. Write each force in terms of its components

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

    [tex]F_1=268\times cos(34\°)\hat i+268\times sin(34\°)\hat j[/tex]

    [tex]F_1=222.18\hat i+149.86\hat j[/tex]

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

   [tex]F_2=487\times cos(68\°)\hat i+487\times sin(68\°)\hat j[/tex]

   [tex]F_2=182.43\hat i+451.54\hat j[/tex]

2. Add the corresponding components

   [tex]F_R=F_1+F_2=404.61\hat i+601.40\hat j[/tex]

The magntitude of the resultant force is:

[tex]|F_R|=\sqrt{(406.61)^2+(601.40)^2}=724.84[/tex] pounds

The angle is:

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

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