Vectors and Equilibrium · 8 min read
Resultant of vectors
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Introduction to vectors
In Physics, some things only have size, like a bag of garri weighing 50kg. But some things have both size and direction, like a bus moving at 60km/h towards Lagos. We call these Vectors.
When two or more forces pull an object at the same time, we need to find one single force that can do the same job as all of them combined. This single force is what we call the Resultant.
In simple terms, it is the 'final boss' vector that represents the total effect of all other vectors added together.
Vectors in the same direction
Imagine you and your friend are pushing a stalled small car (okada or small bus) towards the mechanic shop. If you push with 10N and your friend pushes with 20N in the same direction, you just add them together: 10 + 20 = 30N.
Vectors in opposite direction
Think of a game of tug-of-war. If the boys pull to the right with 100N and the girls pull to the left with 80N, the rope will move to the right with a force of 20N (100 - 80).
Vectors at right angles
When two vectors act at 90 degrees to each other, like one person pulling a box North and another pulling it East, we use the Pythagoras Theorem to find the resultant.
The formula is: R2 = A2 + B2, where R is the resultant and A and B are the two forces.
The Parallelogram Law
Sometimes, vectors act at angles that are not 90 degrees, like 60 or 120 degrees. For this, we use the Parallelogram Law of Vector Addition.
Simply put, if you draw the two forces as sides of a slanted box, the line cutting through the middle is your total force.
Worked example: Resultant of forces at right angles
A man pulls a boat across a river with a force of 3N while the water current pushes it sideways with a force of 4N. If the two forces are at right angles, calculate the resultant force.
1. Identify the forces: A = 3N, B = 4N.
2. Use the Pythagoras formula: R2 = 32 + 42.
3. Calculate the squares: R2 = 9 + 16 = 25.
4. Find the square root: R = square root of 25 = 5N.
Key points
- •A vector has both magnitude and direction.
- •The resultant is the single vector that replaces multiple vectors.
- •Add vectors going the same way; subtract vectors going opposite ways.
- •Use Pythagoras theorem (R2 = A2 + B2) for vectors at 90 degrees.
- •Use the Parallelogram Law for vectors at any other angle.