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Because the cars could be travelling in the same direction, opposite directions and coming towards one another, or opposite directions but travelling away from each other.
So direction is important when we have bodies moving relative to each other, why do you think motorways are designed the way they are?
So almost all quanities involving motion are Vectors, that is they
need a Value and a Direction.
Calculate the the variation of the distance between the cars vs time and represent this on a graph for each scenario.
Take for example gravity, what direction does gravity work?
what happens when you hit a golf ball, kick a football ? how does it fly?
Gravity is an acceleration that always works towards earth, this causes anything lauched up in the air to come back down!
but things can go upwards!
they must overcome the force of gravity and its corresponding acceleration (if only for a short while)
Draw the flight of a projectile (something fired into the air, maybe a basketball, a canonball or a firework)
Question
How could you get a tennis ball to fly
- as far away as possible?
- for the longest time?
What is very important to know is that
Direction Matters,
to any value based on motion, which in turn also applies to Forces.
A Vector is a quanitity (a number) that is also defined by a direction.
The use of vectors helps us calculate the net outcome of two (or more) differerent quantities that have a direction.
Values that are not Vectors are called Scalar values, these values have no direction attached to them.
Common examples of Scalar and Vector Quantities
A visual aid to describe the difference between distance and displacement
The next section to be studied is here
Vectors problems are different to the maths you would have faced before now,
at the beginning these differences can seem trivial
and then as you proceed it might seem complicated,
but in truth neither is the case and with some practice they are actually an easy to use system to resolve problems with forces.
So when writing down a Vector, two things must be considered
1) The size of the Vector (a.k.a. the Magnitude)
2) The direction of the vector, the direction.
The next section to be studied is here
Find resultants using newton balances or pulleys.
A wooden board, pins, newton balances (3 min), some masses, string (fishing line)
- Take a board, using a hammer tap 2 pins, into the board in random locations
- take some of the string into 3 lengths, tie it at a centre point (possibly about a washer)
- Tie all the strings to the Spring Balances
- Attach 2 of the spring balances to the pins.
- To the 3rd balance attach a set of masses.
- Behind the strings make a mark on paper
- Mark the forces on the page too.
- Remove the page, pins balance and start again.
Or here is an applet that does just that
Appropriate calculations.
https://isaacphysics.org/questions/ch_b_p1?board=physicsskills_book_ch_b1
Vector nature of physical quantities: everyday examples.
Forces are vectors, so we can find a resultant force on an object, no matter how many forces are acting on it. If the resultant force is zero, the forces must be balanced.
Balanced forces cause no acceleration (This means that the object will remain stationary or carry on moving at a constant speed.
Vectors are a convienient way for us to represent forces and their interactions in the everyday world. We cannot just add and subtract forces because they all don't work in the same line.
Using Oliver Murphys Fundamental Applied Maths Do the questions on pg 10, 11, 12 & 13
Just to demonstrate the x and y changes with a falling body watch this
http://galileoandeinstein.physics.virginia.edu/more_stuff/flashlets/CompoundMotion.swf
Homework on page 17
there is even more on Vectors here
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