## Tuesday, June 21, 2011

### Speed and velocity

I mentioned as part of GCSE Physics that the guide described the differences between speed and velocity; it has been pointed out to me that I neglected to explain what that difference was. Easily remedied - speed is scalar whereas velocity is a vector; there you go.

Ha no I won't leave you there. In the simplistic terms of the guide speed is just a measurement of distance over time 10mph or 10m/s (magnitude); velocity is the same, but with directionality 10mph North; 10m/s South (magnitude and direction). Big deal why bother with a difference at all?

Consider gravity. I throw a ball straight up and it comes straight back down because it's attracted to the mass of the Earth beneath it; except it's not. It's attracted to the mass directly beneath it and the mass that lies below it to the north and south and east and west and... If I were in a mine shaft it would also be attracted to the mass to my sides and even above me. So why does it still fall downwards?

Because all the forces can be combined as one downward force or cancel out. In the mineshaft the mass pulling the ball to the left is balanced by the mass to its right. The mass below and to its right and below and to its left result in a force pulling it downwards.

If I just said the masses were attracting the ball at 10m/s/s which way would it fall?

The classic example is a boat being pulled in two different directions - 10mph North and 10mph East. At what speed and direction would the boat travel? Draw each velocity so that they make one continuous path and connect the two end points. In this case a triangle giving a result of roughly 14mph (√(10²+10²)) North East.

To make it fun the boat is travelling at 10mph North East against a current of 5mph West while being pushed 2mph North. No matter which order the lines are drawn the result is roughly 9mph 12 degrees North.

So velocity - very important for navigation and forces.