Calc 3 Extra Credit #1 question 4

Question

Two forces, one of 25 ibs, and the other of 40 ibs, act on the same object. If the angle between the forces is 120 degrees, find the magnitude of the resultant force. (resultant force is the vector sum of the two forces.)

Answer 1

Using an x-y coordinate system, make a sketch showing A of 40 units to the right, and B of 25 units at 120 degrees.

In other words, 40 units in +x and 25 units at an angle of 120 degrees from the +x axis (which is -60 degrees from the -x axis)

To add these vectors, first find the x and y components of the B vector:

B_x = -25 cos 60 = -12.5

B_y = 25 sin 60 = 21.65

Next add the 40 unit vector. This is in the plus x direction and thus has no y component. Call the resulting vector "C"---So:

C_x = 40 - 12.5 = 27.5

C_y = B_y = 21.65

Finally, use the Pythagorean theorem to combine the 2 components:

C = √( 27.5² + 21.65²)