The magnitudes and directions of two forces acting at a point P are given. Approximate the magnitude and direction of the resultant vector. (Round your answers to one decimal place.)

Question

The magnitudes and directions of two forces acting at a point P are given. Approximate the magnitude and direction of the resultant vector. (Round your answers to one decimal place.)

5.0 lb,    110°

3.0 lb,    215°

magnitude	lb
direction	°

Answer 1

You can find the graph in this link:

https://drive.google.com/file/d/13F-PkXN1hNJ9l8Mf6DxqLp4NYD92outk/view?usp=sharing

By simply looking it, we know that our magnitude is close to 5 lbs. and the direction angle (θ) is between 90 and 180 degrees because it is located on the second quadrant.

Let’s get the x and y component of each given vector:

For F₁

y₁ = 5 sin (110˚) ≈ 4.968…

x₁ = 5 cos (110˚) ≈ -1.71…

For F₂

y₂ = 3 sin (215˚) ≈ -1.721…

x₂ = 3 cos (215˚) ≈ -2.457…

Σy = y₁ + y₂ ≈ 4.968… + (-1.721…) = 2.978…

Σx = x₁ + x₂ ≈ -1.721… + (-2.457…) = -4.168…

F² = ( Σx)² + ( Σy)²

F² = ( 2.978)² + ( -4.168)²

F² = 26.235…

F ≈ 5.122 lbs.

For the reference angle:

tan θ_o = (Σy) / (Σx) = 2.978 / -4.168 ≈ -0.7145

θ_o = tan^-1(-0.7145)

θ_o = -35.546˚ (Since this is the reference angle on the second quadrant, we have to add 180 degrees.)

θ = -35.546˚ + 180˚ ≈ 144.45˚

*Make sure you don’t round off your numbers until you reach the final answer.