physics question

Question

orces of 80 N at 130 degrees, and 10 N at an angle of 190 degrees, measured counter-clockwise from the positive x-axis, act on an object.

What is the magnitude of the resultant force (in Newtons)?

What is the angle of the resultant force with respect to x-axis? (positive values only)

Answer 1

I will set this up for you, but YOU do the calculations.

 

Find the resultant F_x and F_y.

 

F_x = (80cos130° + 10cos190°) N

 

F_y = (80sin130° + 10sin190°) N

 

The magnitude of the resultant force is

 

F = √(F_x² + F_y²)

 

Plug in the numbers you get for F_x and F_y.  Counterclockwise angle from +x axis is

 

θ = arctan(F_y/F_x)

 

Plug in the numbers.  Be careful with the choice of a quadrant for θ when you evaluate the arc tangent:

 

+/+ quadrant I

+/- quadrant II

-/- quadrant III

-/+ quadrant IV

 

You have everything you need to complete the solution.  Plug in the numbers, do the calculations, and finish from here.