Solve the given problems. Use a ruler and protractor as in Examples 6 and 7. While unloading a crate weighing 610 N, the chain from a crane supports it with a force of 650 N at an angle of 20° from the vertical. What force must a horizontal rope exert on the crate so that the total force (including its weight) on the crate is zero?

Data from Example 6

Two persons pull horizontally on ropes attached to a car that is stuck in mud. One person pulls with a force of 500 N directly to the right, while the other person pulls with a force of 350 N at an angle of 40° from the first force, as shown in Fig. 9.8(a). Find the resultant force on the car.

We make a scale drawing of the forces as shown in Fig. 9.8(b), measuring the magnitudes of the forces with a ruler and the angles with a protractor. [The scale drawing of the forces is made larger and with a different scale than that in Fig. 9.8(a) in order to get better accuracy.] We then complete the parallelogram and draw in the diagonal that represents the resultant force. Finally, we find that the resultant force is about 800 N and that it acts at an angle of about 16° from the first force.

(a) (b) Car 350 N 350 N 40 16 500 N 500 N 800 N Fig. 9.8