Two people pull on spring balances and a third person pulls on a rope attached to a ring as shown in the diagram below:

When balance #1 reads 200 N, balance 2 reads 350 N, the angle between #1 and #2 is 40º, and the ring is stationary. Using the parallelogram method, calculate the force exerted by the person ( #3), who is pulling on the rope.

Step 1: Decide on a scale: 100 N = 2cm is appropriate. Choose a reference direction along one of the vectors, say G:

Step 2: Draw a horizontal line 7 cm long representing G, the 350 N force. Indicate the size and direction:

Step 3: Using a protractor, draw a line 4 cm long at 40º to the start of the arrow. This represents F, the 200 N force. Indicate the size and direction:

Step 4: Mark an arc of radius 4 cm from the terminal point of the 7 cm line using a pair of compasses. Then, set the pair of compasses to 7 cm and mark an arc from the terminal point of the 4 cm line:

Step 5: Complete the parallelogram by connecting the terminal points of the two vectors to the point of intersection of the two arcs. Draw the resultant and measure its length and direction:

Step 6: The resultant of F and G is a force of 520 N directed along a line making an angle of 26º with Fº and 14º with G. The equilibrant, i.e. the force exerted by the third person, R will have the same magnitude but opposite direction, namely |R| = 520 N along a line making an angle of 154º with F and 166º with G.