VCE Physics Unit 2 2008Units and Motionpage 1

VCE Physics Unit 2 2008Units and MotionPage 1

Units

In Physics we use the SI (Système Internationale) system of units. This metric system of units uses the basic units of metre, kilogram, second and ampere (M.K.S.A.).

There are seven basic quantities from which all others are derived.

QuantityUnitUnit Symbol

Masskilogramkg

Lengthmetrem

Timeseconds

Electric currentampereA

TemperaturekelvinK

Luminous intensityCandelacd

Amount of substancemolemol

Derived quantities are derived from the basic quantities by means of a defining equation.

QuantityUnitUnit SymbolDerivation

ForcenewtonNkgms-2

EnergyjouleJkgm2s-2

PowerwattWkgm2s-3

PressurepascalPkgm-1s-2

Electric chargecoulombCAs

EMF (electric potential)voltVkgm2s-2A-1

FrequencyhertzHzs-1

Velocityms-1

Accelerationms-2

The word per in physics means divided by. So instead of saying speed is the metres divided by the seconds, we say metres per second. It is written as or or or ms-1. Also for simplification we use m3 instead of saying cubic metres.

Multiplying prefixes may be used with any unit symbols to indicate decimal multiples or fractions.

Notice the centi (10-2) does not fit into the usual pattern in physics. Soon they will need to create new words to accommodate the amount of memory on computers.

The units of measurement are used so that we can have a scale of things.

The standard unit for measuring a distance is a metre, which is abbreviated to m.

Below is a table of conversions for distance

The standard unit for measuring time is a second, which is abbreviated to s.

Below is a table of conversions for time

Distance and Displacement

Distance

Distance is how we measure the length an object has travelled, when the object has moved from one spot to another.

An example would be how far you travel on the bus in the morning.

Displacement

The displacement of an object is the change in position of the object measured in a straight line from the starting point to the finishing point. Displacement is measured in units of length and it must have a direction that the object has been displaced.

Example 1

A boy and a girl were both at the Beach.

The two had decided to leave the beach and meet up

in the city. The boy went straight to the city and travelled

5 km. The girl went shopping first then went to the City.

The distance the boy travelled was 5 km, the displacement

of the boy was 5 km. The distance the girl travelled was

7 km, and the displacement of the girl was 5 km.

If the girl decided she would rather go and finish

shopping and left the city, what would her total distance

travelled be? What would here total displacement be?

The distance the girl travelled is:

3 km + 4 km + 4 km = 11 km

The displacement now would be 3 km, the distance from

the beach to the shopping centre.

If you do ten laps of a 50m swimming pool, you will have covered a distance of 500m. Your displacement will be zero though.

Speed and Velocity

Speed

The average speed is a measurement of the change is distance within a given change in time.

Average speed

This can be expressed in the formula

Where v = speedd = distancet = time

Since speed is a measurement of the distance travelled over the time taken , it has the units metres per second. Although speed can have any units of distance over time. Eg: kilometres per hour.

You can calculate the distance travelled if you know the speed and the time taken, by using the following formula.

You can also calculate the time taken if you know the speed and the distance travelled, by using the following formula.

Velocity

The velocity, v, of a particle is its rate of displacement. Because displacement has a direction the velocity has the same direction.

average velocity =

Average Velocity from a graph

The gradient of a displacement time graph is the average velocity.

Example 2

What is the average velocity after 10 seconds?

After ten seconds the displacement is 85 metres East.

Using Velocity = displacement / time

v = 85  10 = 8.5 m/s

What is the average velocity from 5 seconds to 9 seconds?

To answer this question we find the gradient of the graph through that region.

Displacement after 9 seconds = 75m East

Displacement after 5 seconds = 35m East

v = change in displacement / change in time

v = (75 East – 35 East) / 4

v = 10 m/s East

Instantaneous Velocity

Instantaneous velocity can be obtained from a velocity time graph. The velocity can be obtained for any instant of time.

Example 3

What is the velocity after ten seconds?

Reading from the graph, the ten seconds point corresponds to a velocity of 10 m/s East.

What is the Velocity after 30 seconds?

Reading from the graph, the thirty seconds point corresponds to a velocity of 20 m/s East.

Acceleration

Acceleration is the term given when a body undergoes a change in velocity within a given change in time. The acceleration of a body can be calculated by the using following formula:

Average Acceleration =

Acceleration is normally given the symbol a, and it has the units ms-2.

The way you get a change in velocity is by subtracting the Initial Velocity from the Final Velocity

Change in Velocity = VFinal - VInitial

You can now write the formula asAverage Acceleration =

Acceleration is a vector, this is because if a body is accelerating, it must be accelerating at a given rate (magnitude) and it must be accelerating in a direction.

So the average acceleration is the gradient of a Velocity time graph.

Example 4

Calculating the acceleration in the first 20 seconds.

The gradient of the line it the acceleration, this is calculated by the rise over the run.

Which is: Average Acceleration =

The average acceleration for the first 20 seconds = 1 ms-2

Example 5

Calculating the acceleration from the 20-second point until the 35-second.

Average Acceleration = So the average acceleration for this time period = 0 ms-2

Example 6

Calculating the acceleration from the 35-second point until the 50-second point.

Average Acceleration = So the average acceleration for this time period = -1.33 ms-2

Because the acceleration on the body is negative, it can be described as decelerating.

Example 7

Calculating the acceleration from the 0-second point until the 50-second point.

Average Acceleration = So the average acceleration for this time period = 0 ms-2

Because the total change in the velocity is zero, it can be said that the average acceleration on the body is zero.

Equations of motion

Let a particle commence with an initial velocity of 'u' and move with a constant acceleration 'a' in a straight line. Let 'x' be the displacement during the time 't', and 'v' the velocity at the end of this time.

Below is a proof for the formulas of motion; you will not be expected to reproduce them in anyway.

Acceleration = a =

at = v - u

v = u + at

Displacement = average velocity × time

x = (u + v) × t

Since x = (u + v) × t

x = ut + vt

x= ut + (u + at)t

x = ut + ut + at2

x = ut + at2

Since x = (u + v) × t

x = ut + vt

x= (v-at)t + vt

x = vt + vt - at2

x = vt - at2

If v = u + at

v2 = (u + at)( u + at)

v2 = u2 + 2uat + a2t2

v2 = u2 + 2a(ut + at2)

v2 - u2 = 2ax

So the 5 formulas for analysing motion with constant acceleration are:

The formulae

These are the five equations of motion. Each equation uses 4 of the 5 different variables. Each equation uses a different combination of the 4 variables.

These formulas can also be derived from the graphs.

Technique for solving SLM problems using the equations.

1. Use a sign convention for all values, ie. take one direction as positive.
2. List all the headings:u = v = a = t = x =
3. Substitute the values that are given. (Generally 3 will be given, 1 required and 1 not needed).
4. Check if u = 0, or v = 0.
5. Select the relevant formula and substitute, then solve.

Vertical motion under gravity

Falling bodies are an example of motion under a constant acceleration. The acceleration due to gravity is considered to be 10 ms-2. When solving problems with gravity, substitute 'g' for 'a'.

You will need to be careful with your directions when doing vertical motion, on the way up the object slows down because the acceleration is in the opposite direction to the velocity, but on the way down the acceleration and velocity are in the same direction, so the objects velocity increases. At the top of the flight, the velocity is zero, but the acceleration is still 'g'.

Centre of mass

Most structures are constructed of many different parts and are quite complex. They can be simplified by imagining that the gravitational force on the entire structure was acting at just a single point called the Centre of Mass or Centre of Gravity of the structure. The centre of mass is the balance point for a structure. Imagine a see-saw, the balance point is the middle of the beam.

Stability of structures

As the centre of mass is a balance point, an object is unstable if a vertical line through its centre of mass does not pass through its base.



stableunstable falls back falls over

A structure is stable if the centre of mass is over the base. The width of the base and the height of the centre of mass affect the stability of a structure. To increase the stability, the centre of mass can be lowered and the width of the base increased.