IDNLearn.com is your go-to resource for finding expert answers and community support. Get accurate and timely answers to your queries from our extensive network of experienced professionals.

Resultant Force Forces with magnitudes of
125 newtons and 300 newtons act on a hook (see
figure). The angle between the two forces is 45°. Find
the direction and magnitude of the resultant of these
forces. (Hint: Write the vector representing each force
in component form, then add the vectors.)


Sagot :

The resultant of the two forces is 398.32 N and the direction is 12.8⁰.

The given parameters:

  • first force, F₁ = 125 N at 45⁰
  • second force, F₂ = 300 N at 0⁰

The vertical component of the forces is calculated as;

[tex]F_y = 125 \times sin(45) \ + \ 300 \times sin(0)\\\\F_y = 88.388 \ N[/tex]

The horizontal component of the forces is calculated as follows;

[tex]F_x = 125 \times cos(45) \ + \ 300 \times cos(0)\\\\F_x = 388.388 \ N[/tex]

The resultant of the two forces is calculated as follows;

[tex]F = \sqrt{F_y^2 + F_x^2} \\\\F = \sqrt{88.388^2 + 388.388^2} \\\\F = 398.32 \ N[/tex]

The direction of the forces is calculated as follows;

[tex]\theta = tan^{-1} (\frac{F_y}{F_x} )\\\\\theta = tan^{-1}(\frac{88.388}{388.388} )\\\\\theta = 12.8\ ^0[/tex]

Learn more about resultant forces here: https://brainly.com/question/11194858

View image Onyebuchinnaji