## Uniform Electric Fields

If you can do gravity, you can do electrostatics. They are both inverse square laws for non-uniform fields and behave similarly for uniform fields too.

Remember this diagram? This time, imagine two parallel metal plates – very large, separated by a few mm in air. A primitive capacitor, in other words. The top plate is positively charged by connecting it to the + terminal of a battery and electrons from earth will be attracted to the bottom plate. Because the charges are all of the same kind on each plate and the surfaces are flat, they spread out as far as they can, like a carpet. Now, imagine a charge of  say +3mC (in blue) somewhere in between the plates. It’s experiencing a downward force, repelled by the top plate and attracted to the bottom one. This is quite a large blob of charge, since an electron has a charge…

View original post 405 more words

## Gravitational Fields 2. Non-uniform (radial) Fields

This post follows on from this earlier one which introduced Newton’s Universal Law of Gravitation.

An object with mass creates a gravitational field around it sucking mass towards it – like a whirlpool. Imagine a paper boat. It will always be pulled towards the centre of the hole.

The gravitational field strength (vector) g is defined as the gravitational force at a given point divided by the mass of an object at that point so g=F/m

On earth g = 9.81Nkg-1 (acc due to gravity). Slightly variable, equatorial r >polar r, thus g greater at the poles, neglecting the spin of the earth which will tend to reduce effective value.

g = constant near the Earth’s surface, falls as as we move away.

Gravitational field lines (parallel) are perpendicular to equipotential surfaces (zero change in GPE  when moving around on them, i.e, the field is conservative. The same work…

View original post 333 more words

## Resolving Vectors down a Slope (plus a little bit about friction)

Sometimes, it’s just convenient to represent a single vector by TWO vectors at right angles to each other. Take a look at this diagram. It isn’t a free-body diagram, since I have included resolved components. A FBD would only show W and R

This isn’t labelled very well, I ought to have said that W means ‘weight’ which is equal to ‘mass x g’, but it muddles the diagram. If I now resolve W into two mutually perpendicular components, in red, Wsinθ acts down the slope and Wcosθ acts perpendicular to it. It is Wsinθ which causes the body to accelerate down the slope.When there is no sliding occurring, the frictional  force can have any value from zero up to a maximum value of FR as given in the below equation. If the slope become so steep that the object is moving then the coefficient of static friction is replaced by the smaller coefficient of dynamic friction. (We know how much easier it is to keep a car moving when we’re pushing it than to get it moving in the first place.)

If  this is large enough, the body starts to slide down the slope  The green vector, R is the NORMAL REACTION. This is numerically equal to Wcosθ but always acts AWAY FROM A SURFACE. It is an electrostatic force since if two bodies are touching, their electron clouds overlap a little bit and charges in both bodies are pushed apart. The charges tend to resist being separated hence exert a force to prevent this happening. Weight is of course, gravitational, so these two forces are NOT Newtonian pairs.

A Newtonian Pair of forces is one in which the forces are:

* equal and opposite

* act on different bodies

* are of the same KIND ( 4 available – gravitational, electromagnetic, strong nuclear, weak nuclear)

The pull of the Earth on the Moon (and vice-versa) is an example of a Newtonian pair.

Here’s a link to this idea used in practice-finding the acceleration of a body down an inclined plane.

You should be able to think of at least four vector quantities (size plus direction) and four scalar quantities (size only). If you can’t, look here.

You can’t just add numerically when you want to add two or more vectors (of the same kind, obviously) since a push of 1N to the left when added to a pull of 3.5N to the right results in a pull of 2.5N to the right. We have to take direction into account.

But, what if they don’t act along the same straight line? There are several methods for adding lots of them together. The head-to-tail method is one. A vector is just a line on a piece of paper of a particular length which represents its size with an arrow on it to indicate direction.  Adding two vectors A and B is quite simple. Take the tail of B and put it on the head of A. The vector sum is found by the line joining the tail of A and the head of B. Works for as many vectors as you like.

In more detail, the head-to-tail method involves drawing a vector to scale on a sheet of paper beginning at a designated starting position. Where the head of this first vector ends, the tail of the second vector begins (thus, head-to-tail method). The process is repeated for all vectors that are being added. Once all the vectors have been added head-to-tail, the resultant is then drawn from the tail of the first vector to the head of the last vector; i.e., from start to finish. Once the resultant is drawn, its length can be measured and converted to real units using the given scale. The direction of the resultant can be determined by using a protractor and measuring its angle of rotation – in my example anticlockwise from due East, but clockwise from North can also be used. Just specify.

A step-by-step method for applying the head-to-tail method to determine the sum of two or more vectors is given below.

1. Choose a scale and indicate it on a sheet of paper. The best choice of scale is one that will result in a diagram that is as large as possible, yet fits on the sheet of paper.
2. Pick a starting location and draw the first vector to scale in the indicated direction using a ruler and protractor. Label the magnitude and direction of the scale on the diagram (e.g., SCALE: 1 cm = 20N for adding forces, for example).
3. Starting from where the head of the first vector ends, draw the second vector to scale in the indicated direction. Label the magnitude and direction of this vector on the diagram.
4. Repeat steps 2 and 3 for all vectors that are to be added.
5. Draw the resultant from the tail of the first vector to the head of the last vector. Label this vector as Resultant or simply R.
6. Using a ruler, measure the length of the resultant and determine its magnitude by converting to real units using the scale (4.4 cm x 20N per cm = 88N. Here’s an example:

## Graphs and Error bars (IB)

Original post is here.

In your MYP or IG course you should have been told to use a sharp pencil to draw a small cross to represent a data point on a graph, or a dot with a ring round it. The diameter of the ring should represent the error in the reading.

In IB, we do things more precisely.

Error bars show the actual uncertainty above and below the data point. They can be errors in either the dependent x or the independent y variable or both. In the following example we’ll only concern ourselves with an uncertainty in y.

Suppose we want to try to plot a graph of the speed of a car, starting from rest for the first few seconds. If we try to read off the numbers on the speedometer and write them down, there’ll be a lot of uncertainty in the result. Nevertheless, let’s try just to see…

View original post 251 more words