Stage 6 Physics – Moving About

Why do head on crashes cause so much damage?

What is moving?

Is the car moving? Is the road moving? Is the snow moving? Are you moving?

What is moving?

If you are in an elevator without signs or lights, how do you know if you are going up or down or that you are moving at all?

It’s all relative

Velocity is measured according to a frame of reference.

We usually talk about velocity being relative to a stationary Earth.

But the Earth is moving at 30 km s-1

around the sun, and the sun is orbiting around the centre of the galaxy.

There is no absolute rest frame of reference.

Relative velocity

Relative velocity is the velocity of an object measured by a moving observer.

The relative velocity is the difference between the velocity of the object relative to the ground and the velocity of the observer relative to the ground.

Relative velocity - example You are in a car travelling at a

constant velocity of 90 km h-1 west on a straight road. The car ahead of you is travelling at a constant speed of 100 km h-1 in the same direction.

100 km h-1

90 km h-1

Relative velocity - example What is the car’s velocity relative to the ground?

100 km h-1

What is the car’s velocity relative to you?

Remember: relative velocity is the difference between the velocity relative to the ground and the velocity of the observer relative to the ground.

We will make west + and east -.

100 km h-1 – 90 km h-1 = 10 km h-1.

Since the answer is positive, and we made + west, the relative velocity of the car to you is 10 km h-1 west.

Relative velocity – another example You are driving at 90 km h-1 west. Another car

is travelling towards you at 100 km h-1 east.

Relative velocity – another example

What is the car’s velocity relative to you?

Let’s say west is + and east is -. So your velocity is +90km h-1 and the car’s velocity is -100 km h-1.

Relative velocity = object’s velocity relative to the ground – observer’s velocity relative to the ground.

Relative velocity = -100 km h-1 – 90 km h-1

= -190 km h-1

= 190 km h-1 east

Head on collisions

This is why head on collisions cause so much damage – the relative velocities add together!

If you’re travelling at 60 km h-1 and you hit a car travelling towards you at 60 km h-1, the car’s relative velocity towards you will be 120 km h-1.

Vector addition

Remember: vectors are quantities with a magnitude and a direction.

We can represent vectors such as displacement, velocity and acceleration with vector diagrams (they are just arrows)

Vector addition

Arrows need to be to scale.

Every vector arrow has a tail end and a tail head.

Basically, instead of describing object’s displacement/velocity/acceleration/force in words, we use vector diagrams to indicate magnitude and direction.

This vector has half the magnitude of the other vector

This vector has twice the magnitude of the other vector

Tail end Tail head

Vector addition

We use vector diagrams to visually represent word problems.

It is easier to draw arrows to show magnitude and direction and to write a whole paragraph.