Vectors and Scalars - What's the Difference, and Vector Addition

Vectors and Scalars - What's the Difference, and Vector Addition

Vectors and Scalars are two types of measurements you can make.

  • A scalar measurement only records the magnitude (or amount) of whatever you are measuring.

  • A vector measurement records the magnitude of the thing you are measuring and the direction.

Vectors and Scalars

A simple example is to consider a force. If you are standing at the edge of a swimming pool and you experience a sideways force of 100N, the direction of the force really matters. If it's towards the pool - splash! If it's away from the pool, you're OK. So force is an example of a vector.

Put the following measurements into the correct column in the table:

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Notice the difference between distance and displacement:

A Formula One car starts a race from the pits and finishes it two hours later in the same pits. It has covered a distance (scalar) of 250 km in the meantime but it is at the same spot that it started from so it has a displacement (vector) of zero!

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Adding scalars is easy because you can just add the numbers.

For Example: 3kg + 4 kg = 7 kg

Adding vectors needs much more care. You have to take into account their magnitude and direction.

For Example: What's 3N + 4N? Well, it depends on the directions! Look at the possibilities...

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Or

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(Note: 1N is not balanced)

Or

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So in other words, you add vectors geometrically (using geometry). You should be able to do this using accurate diagrams (don't forget your protractor) or by using Pythagoras.

The resultant vector is the one that you get when you add two or more vectors together. It is a single vector that has the same effect as all the others put together. Finding the resultant vector when the forces are in different directions can be tricky if you don't like Pythagoras, so here's a couple to get you going!

Worked Example:

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Using Pythagoras: R2 = 82 + 72

So, R = √113 = 10.6 N

Question:

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