Question

A force

F1

of magnitude 6.90 units acts at the origin in a direction 40.0° above the positive x axis. A second force

F2

of magnitude 5.00 units acts at the origin in the direction of the positive y axis. Find graphically the magnitude and direction of the resultant force

F1 + F2.

magnitude units

direction ° counterclockwise from the +x axis

An illustration shows a square wooden crate, on which two force vectors, vector F1 and vector F2 are acting. The force vector F1 is acting at an angle θ to the horizontal, while the force vector F2 is acting vertically to the crate.

Answer 1

So the net force, F = F1 + F2
= 5.286 + (4.435 + 5)
= 5.286 + 9.435
Magnitude, |F|
= SQRT[(5.286)² + (9.435)²]
= 10.81 units

tan = 9.435/5.286
= tan^-1(9.435/5.286)
= 60.74 degrees
Graphically, you can measure the angle between F1 + F2 and x-axis