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December 13, 2019, 03:09:57 am

Author Topic: Scalars and Vectors  (Read 138 times)

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Bri MT

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Scalars and Vectors
« on: June 21, 2019, 05:48:27 pm »
+5
In this section of the syllabus, the following stimulus question is provided: if I start in the middle of the oval and walk 100 metres where could I end up?

The most obvious answer to this might be 100m away, but it’s not the only answer; they could have walked 25 metres to the east then 75 metres west, or they walked 50 metres north then 50 metres south. Assuming there are no obstacles in their path they could be anywhere inside a circle with radius of 100 metres centred on their start point.

However, if we were told that not only did they walk a distance of 100 metres but they also had a displacement of 100 metres east, we would know that they walked in a straight line without turning around and were 100 metres to the east of where they started.

This is because distance is a scalar, and therefore considers only the magnitude of the path taken, whereas displacement is a vector, and therefore describes the direction and magnitude between the start and end points.


Below I've made a list of vectors and scalars that answer common questions:
How far did it go?
scalar: distance (eg. 100 m)
vector: displacement (eg. 100 m east)
How fast did it go?
scalar: speed (eg 5 m/s)
vector: velocity (eg 5 m/s west)
How quickly did it change velocity?
vector: acceleration (eg. 5 m/s^2 west)
How long did it take?
scalar: time (eg. 5 s)
How big was it?
scalar: mass (eg. 2 kg)
What force was applied?
vector: force (eg 5 N east)
How hot was it?
scalar: temperature (300 K)


Combining vectors:
It’s simple to add vectors going in the same direction: if someone has travelled 40 m east, then 30 m east, you know their displacement is 70 m east (40+30 = 70). On the other hand, if someone has travelled 40 m east then 30 metres west they’ll be 10 metres from where they started and have a displacement of 10 m east (40 – 30 = 10). And finally, if they have travelled 40 metres east then 30 metres north they’ll be 50 m away and roughly to the north east.

To figure out the exact distance and angle, we can draw up a right-angled triangle with side lengths of 40m and 30m. We then calculate the hypotenuse as 50m using pythag and use the tangent function to find our elusive angle. We then report the angle (53 or 47 degrees) in our answer relative to the direction we are measuring our angle from.


This may sound overwhelming, but with this topic practice is well and truly the key success – and if you do lots of questions you’ll gain confidence in no time :)


If you have any questions or ways of thinking about this that help you please feel free to comment below :)
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Bri MT

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Re: Scalars and Vectors
« Reply #1 on: July 20, 2019, 11:07:02 pm »
+1
Adding a link to Rui's explanation of how to calculate vectors for specialist maths as you can use the exact same approach for physics :)
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