A pushes with force of 300 N at 25 degrees. B pushes with force of 275 N at 160 degrees. C pushes with force of 325 N at 300 degrees. Find resultant force.
I got 187 N at -19 degrees or 161 degrees. Correct? or could you explain more please? Thank you.
To find the resultant force, we need to find the horizontal and vertical components of each force, and then add them up separately.
Let's break down each force into its horizontal and vertical components using trigonometry:
Force A:
- Horizontal component (Fx_A) = 300 N * cos(25 degrees)
- Vertical component (Fy_A) = 300 N * sin(25 degrees)
Force B:
- Horizontal component (Fx_B) = 275 N * cos(160 degrees)
- Vertical component (Fy_B) = 275 N * sin(160 degrees)
Force C:
- Horizontal component (Fx_C) = 325 N * cos(300 degrees)
- Vertical component (Fy_C) = 325 N * sin(300 degrees)
Note: Be careful with the angles in trigonometric functions. Some functions work with radians and some work with degrees. In this case, make sure to use the appropriate function for the unit being used.
Now, add up the horizontal and vertical components separately:
Total horizontal component (Fx_total) = Fx_A + Fx_B + Fx_C
Total vertical component (Fy_total) = Fy_A + Fy_B + Fy_C
Finally, use the Pythagorean theorem to find the magnitude of the resultant force and inverse tangent function to find its direction:
Resultant force (F_total) = √(Fx_total^2 + Fy_total^2)
Direction (angle) = tan^(-1)(Fy_total / Fx_total)
Calculate these values using a calculator or a software. If you have done the calculations correctly, you should get a resultant force of approximately 187 N at an angle of -19 degrees or equivalently 161 degrees.