Vectors

Q4. Find the resultant of two forces (80 N and 40 N) acting at an angle of 120° to each other.

What is the angle between the resultant and the first force?

Using graph paper you can construct the vector diagram as shown above.

Make sure that you clearly indicate the scale you are using for the vector magnitude.

Also make your answer stand out clearly to the examiner.

First sketch a diagram

To tackle the problem by calculation we can use the cosine rule

a² = b²+ c² − 2bc cos α

R² = 80² + 40² - 2 x 40 x 80 x cos (180 - 120)^o

R² = 6400 + 1600 - 6400 x cos 60^o

R² = 8000 - 6400 x 0.5

R² = 8000 - 3200 = 4800

Resultant force R = 69 N

The angle between the resultant and the first force (80 N) on our diagram is γ

Using the sine rule we have:

sin γ/40 = sin 60^o/69

sin γ = sin 60^o x 40/69

sin γ = 0.866 x 0.580 = 0.50

γ = 30^o