Activity # 5 of the first portfolio Vector Addition Problems

Analytical method to add vectors: Rectangular component method or just the component method.

Summary

The component method of addition can be summarized this way:

Using trigonometry, find the x-component and the y-component for each vector. Refer to a diagram of each vector to correctly reason the sign,

(+ or -), for each component.

Add up both x-components, (one from each vector), to get the x-component of the total.

Add up both y-components, (one from each vector), to get the y-component of the total.

Add the x-component of the total to the y-component of the total then use the Pythagorean theorem and trigonometry to get the size and direction of the total.

Exercises

1. Determine the resultant vector of the addition of the following vectors:

A = 3 units, 40°, B = 6 units, 150° and C = 2 units, 70°. 7.2 units at 108°

2. A car travels 20 mi at 60º north of west, then 35 mi at 45º north of east.

3. Vector A has a length of 3.76 cm and is at an angle of 34.5 degrees above the positive x-direction. Vector B has a length of 4.53 cm and is at an angle of 34.1 degrees above the negative x-direction. What is the sum (resultant) of the two vectors?

4. Three vectors are added, 36m, 34° north of east and 23 m, 64° W of N. Determine the resultant vector (magnitude and direction of course) 31.5 N of E

5. Cameron Per (his friends call him Cam) and Baxter Nature are on a hike. Starting from home base, they make the following movements.

A: 2.65 km, 140°, B: 4.77 km, 252° and C: 3.18 km, 332°.

Determine the magnitude and direction of their overall displacement. 4.38 261°

6. A ship leaves harbour H and sails 6km north to port A. From here the ship travels 12km east to port B, before sailing 5.5km south-west to port C. Determine the ship's resultant.

7. Three vectors A, B, and C are shown in the figure below. Find one vector (magnitude and direction) that will have the same effect as the three vectors shown in the same figure. 71.8 N at 139.9°

8. Three ropes are tied to a small metal ring. At the end of each rope three students are pulling, each trying to move the ring in their direction. If we look down from above, the forces and directions they are applying are shown in Fig 011. Find the net force on the ring due to the three applied forces. 53.8 lb at 197.16°

9. Write down and solve the problem 17 of your workbook on page 31 (You must include the figure 1.28).

10. Find the magnitude and direction of the resultant force of the following forces F1 = 70 N at 45°, F2= 40 N at 90°, F3=50 N 120 ° and F4=90 N at 330°.

11. Challenge.

The five forces shown in Fig. P-314 are in equilibrium. Compute the values of P and F.