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13/12/05 J6

We sat the test - answers on Thursday.

Momentum was introduced.

07/12/05 J6

We looked at a method for answering each statics type question.

1. Draw a diagram(s), to allow you to solve the problem (e.g. situation diagram, free body force diagram, tip to tail vector addition diagram.)

2. State the principal(s) you are going to use.

3. Quote any necessary formulae you are going to use. e.g. moment = force * distance

4. Under the correct heading (e.g. "anticlockwise moments") fill in the relevant numbers

5. Calculate your answer - remember units and do not give your answer to any more degree of accuracy than the information given to you in the question.

HW Revise - another go at a test on Newton's 3 laws, resolving forces and moments.

01/12/05 J6

More on resolving forces and we just started to go through a difficult Q11 from a new handout which included moments aswell.

HW Q12 from the same handout. Remember:

1. Make vertical forces equal

2. Make horizontal forces equal

3. Make clockwise and anti-clockwise moments equal.

29/11/05 J6

The performance in the test was totally abysmal. We went through it in detail and then went back to practise yet more questions on resolving forces. We will recap Newton's laws and moments and then try again with another test. I will not continue with the course until the vast majority of you achieve an acceptable level of understanding for statics.

HW Finish the booklet of resolving forces questions up to question 8.

Yellow cards will be issued immediately after the lesson for this one, cracking down is clearly required.

Alex - This link contains the pdf file with the homework questions, have a go please.

24/11/05 J6

We sat the test.

22/11/05 J6

We did a set of practise statics questions.

Simply balancing moments about a point and vertical and horizontal forces can allow you to find unknown forces with great ease.

HW Finish that set of questions to revise for a test which will be sat on Thursday.

17/11/05 J6

We had a lesson a little before I disappeared to CCF camp. Quite what happened I can't really remember but it will have been to do with solving 2-D statics problems. Conditions for equilibrium are:

1. Forces are balanced in all directions

2. Moments are balanced clockwise and anti-clockwise.

You can form 3 equations from these conditions: vertical balanced forces, horizontal balanced forces and equal moments about any point you choose on an object.

(in fact, the 2 directions need not be vertical and horizontal, but must just be at right angles to each other.)

HW Probably.

15/11/05 J6

We solved an equilibrium problem. Equilibrium is where there is no overall force acting on a body.

Draw all the force vectors acting on a body in equilibrium nose to tail and you will get no resultant force. Therefore a closed shape (polygon) will be produced.

This site has more detail on this idea.

We did some problems based on an object sitting on an inclined plane. You must be happy to do simple geometry to work out angles and such like.

Follow the link for some examples of this.

Finally we went on to look at the turning effect of forces. (Moments or torques).

Moment = Force * Perpendicular distance from pivot point

This is fairly straightforward stuff, but you also need to know about couples, which are 2 opposing forces that act through different lines. The moment of a couple is equal to the size of the force multiplied by the perpendicular separation between their lines of action.

In this case Moment = 2sF

For objects in static equilibrium, not only do all of the forces acting in each direction have to add up to zero, the turning forces clockwise and anti clockwise about any point must also be zero.

We solved some lorry on a bridge problems based on this idea.

HW HAnd in Chapter 22 Qs for next time.

10/11/05 J6

We missed the double lesson due to prize day. Today we cleared up a few loose ends on types of forces. You must be aware of what to label each force in your force diagrams.

There are 4 fundamental forces in the universe:

1. Gravity - attraction that all mass feels towards all other mass.

2. Electromagnetism - this encompasses both electrostatic and magnetic forces.

3. The strong nuclear force - holds atomic nuclei together, it only acts at very short range

4. The weak nuclear force - also acts within the nucleus.

However, there are also a number of other forces called contact forces which need classification.

Contact forces between solid objects are usually split up into the normal reaction force which acts at 90 degrees to surface and a tangential contact force which we know as static friction.

Solids sliding past each other experience friction. Objects moving through fluids (liquids or gases) experience drag forces. An object immersed in a fluid experiences an upthrust which is equal in size to the weight of displaced fluid. Fast moving fluid exert less pressure than slow moving fluids and so a wing shape moving through a fluid generates aerodynamic lift.

As long as you are happy to mention and use all of the above terms when labelling forces in diagrams, things are likely to be fine.

HW Do 20.1.3.4.5 for next time.

03/11/05 J6

When adding vectors together which are not perpendicular or parallel to each other, it is a much easier problem to solve if you find the vertical components of both vectors and add them together. This is the total vertical component of the combined vector. Then find the horizontal component of both vectors and add them together to find the total horizontal vector.

You can then combine the total vertical and horizontal components to find the size and direction of the total vector using Pythagoras' theorem and trigonometry.

Seriously, this is much easier than using the cosine rule.....

We did some AS level practise questions on vectors.

HW The practise questions should be finished by next week. Those with half term and other gaps need to fill them by tomorrow.

01/11/05 J6

We looked at adding vectors together. This is necessary when trying to calculate a resultant force, velocity or any other vector quantity.

The classic question is when trying to swim across a river. You swim through the water with a certain velocity v₁, but the water itself is moving relative to the land with velocity v₂. Therefore your velocity relative to the land is your water velocity plus the river's velocity.

v₁ + v₂ = v₃

Pythagoras and trigonometry must be used to work out the length and direction of the resultant vector. More details here

and some good problem solving here.

We also looked at finding the components of a vector. This involves finding 2 perpendicular components of a vector which is not acting at a convenient angle for problem solving.

Often this means seperating out horizontal and vertical motion (constant acceleration equations can then be used seperately for each motion)

Finding the components of a vector to help solve a problem is called resolving a vector.

More on this here.

We'll look at this more next time.

HW I need the half term work in from everybody without fail, also chapter 8, 11 and 12/13 questions which were set a while back form all. Necessary so I can be nice about you to your parents please. Also, the OCR sheet with 2 questions on resolving vectors please.

20/10/05 J6

Oh my word. "Free body force diagrams" and their even more contrived partners "situation diagrams" were covered. (Check it out, here's a whole website on them). I hope never to mention them again, we'll just draw in the forces acting on a body if we need to.

The wonderful text book was also at pains to let us know that Newton's 1st law "A body will remain at rest or continue to move with a constant velocity as long as the forces remain balanced" is different from Newton's 3rd law "While body A exerts a force on body B, body B exerts an equal and opposite force, of the same type, on body A".

Glad they cleared that one up for us then......

HW A nice set of A level type motion questions for you to solve.

18/10/05 J6

We used trolley track this time to better effect. We tested Newton's 2nd law, F = ma by varying the mass and then the force on a system and measuring its acceleration.

HW Finish the graphs from both experiments.

We also started off on Newton's 3rd law. The common statement of this rule "every action has an equal and opposite reaction" can be misleading.

In reality "When body A exerts a force on body B, body B exerts an equal and opposite force of the same type on body A"

So the N3 reaction to the Earth pulling down on you (your weight) is actually the gravitational force which you exert on the Earth. The force affects a small mass like you quite a lot, but is pretty irrelevant for a mass the size of the Earth.

So is a body is in equilibrium, the equal and opposite forces which are acting on it are not a Newton 3 pair.

13/10/05 J6

We went through the test. Many of you were reluctant to use the motion equations for constant acceleration that were given to you. They are the easiest way to solve the problems!

We will use the air track again on Tuesday to do an experiment to verify Newton's 2nd law. Newton's 1st law is pretty straightforward. You must learn the exact statements of the law as given in the book to avoid any confusion come the exam.

Newton 2 is basically F=ma.

HW Do 12.4, and 13.3-13.5 on N1 and 2

11/10/05 J6

We sat the past paper test, we'll go through that next time.

An experiment designed to confirm Newton's 2nd law quite frankly didn't work. The idea was to show that the acceleration of an object is proportional to the force acting on it (F=ma)

We'll try a different version of the same thing next week possibly.

06/10/05 J6

We did some of the assessment questions from the book. I'll do a short test for next time (30 or 40 mins) on everything covered so far (but not the SI units stuff).

HW Revise.

04/10/05 J6

We talked about mass and there are 2 features that it has. It is harder to accelerate something which contains more matter (inertia), and gravity pulls harder on something with more matter. These 2 factors exactly cancel each other out such that all objects fall at the same acceleration in a gravitational field. (as long as air resistance can be ignored.)

The constant acceleration equations can be applied in this case. we practised some examples - use the standard method and make sure you have directions noted for all vector quantities.

We also looked briefly at the seperation of horizontal and vertical motion. Horizontal motion carries on unaffected by any vertical acceleration that is going on.

A bullet fired horizontally from a gun on a flat plain will hit the ground at the same time as a bullet which is simply dropped simultaneously.

A monkey is doomed if it lets go at the same time as the gun is fired (if you are clever, try to prove that this is true for any angle that the gun shoots at the monkey, not just horizontally as we talked about in the lesson.)

HW Do 11.3-11.5, questions on horizontal projection.

29/09/05 J6

We tried some practise questions which utilised the equations of motion for constant acceleration. We will do enough of these questions to try and remove any doubts from your mind as to how to approach them. Using a the same method to solve these problems each time will always get you to the right answer.

x = vt - 1/2at²

above is another possible (5th) equation which can be used and is entirely equivalent to x = ut + 1/2at²

HW The first 3 sides of the AS motion questions sheets.

27/09/05 J6

We derived the equations of motion for constant acceleration. They are all based upon 2 physical concepts.

Average velocity = Displacement / Time = x/t

Because acceleration is constant, average velocity is simply a mean value.

Average velocity = (u + v)/2

u = initial velocity

v = final velocity

So, (u+v)/2 = x/t or x = t(u+v)/2

Also, acceleration = rate of change of velocity = (v-u)/t

This can be re-arranged to: v = u + at

Substituting one equation into the other, firstly for v and then for t will give you the remaining 2 equations of motion.

x = ut +1/2at²

v² = u² + 2ax

You aren't required to derive these equations at will, but you should understand where they come from.

To successfully solve all motion problems you simply follow this recipe.

1. List all quantities x,u,v,t,a

2. Fill in all quantities given to you

3. Choose an equation which includes only one unknown, along with figures you do know

4.Solve it!

Here are the 4 equations you can use again:

x = t(v+u)/2

v = u +at

x = ut +1/2at²

v² = u² + 2ax

HW Try all the Old chapter 9 practise questions. Use the method if in any doubt, it can't go wrong.

Cheehan's question was solvable using the constant acceleration equations, but created 2 simultaneous equations which required subsequent solving. The answer was 3m per floor.

22/09/05 J6

Ah, you did better in the next HW. tfft

We looked at the motion graphs for a bouncing ball. Important points were:

• The ball has a constant acceleration of about 10m/s/s down except when it it actually in contact with the floor.

• Each succesive bounce is not as high as the previous one (as shown on x/t graph)

• The speed reached just before hitting the ground decreases after each successive bounce.

• The time taken after each bounce, before hitting the floor again decreases over time.

You must be able to determine the relevant velocity and acceleration graphs for this displacement one.

7.2-7.5 + ass. 3 were taken in.

HW Practise Qs 8.2-8.5 (same in both books)

20/09/05 J6

The last HW was done pretty terribly. Changing any quantity into SI base units is a skill you need to acquire. This is mainly for testing equations for homogeneity with respect to units.

Acceleration must take into account the vector nature of velocity. We looked at an example where the direction had changed. Using just the speed in this case would give you a wrong answer. Choosing a direction to be positive before the calculation is therrefore important

We looked at motion graphs. The main difference to what you have all covered before is that there the vector nature of displacement, velocity and acceleration have to be taken into account at A level.

A Java applet showing x, v and a on the same axes.

Bit kiddy, but good revision of the shape of velocity/time graphs.

For many kinetmatics (motion) problems, it is a good idea to be able to sketch any of the 3 motion graphs.

When acceleration is constant, finding out things about motion becomes very easy indeed. We looked at the example of falling under gravity. 2 measurements, distance travelled and time taken allowed us to estimate the acceleration due to gravity.

HW Old Practise Qs 7.2-7.5 and New Assesment question 3

15/09/05 J6

We looked at ticker tape timers as ways of measuring speed. They cannot measure velocity, so their use tends to be confined to one dimensional experiments.

You attempted to use the timers to measure the acceleration due to gravity in the lab. This was something you would have done before in the 3rd and 4th form.

Acceleration = Change in speed/time

HW New book Practise Qs 5.2, 5.5 and Qs 6.1 and 6.2

13/09/05 J6

We looked at a couple of examples of checking equations to see if they are homogeneous with respect to units. This basically involves converting both sides into only SI units (meters, kg, seconds, Amps, moles, Kelvin) and seeing if they end up the same.

We also saw how a micrometer works, in case you ever come across one.

We then moved onto Mechanics proper. The first major point was to differentiate between vector and scalar quantities.

Vector quantities have a direction associated with them aswell as a magnitude (size), whereas scalars only consist of a magnitude.

Distance is a scalar; displacement is the equivalent vector. Speed is a scalar; velocity is the vector. Acceleration is also a vector quantity.

We saw a light gate that can be used to measure speed. It is very difficult to measure instantaneous speed or velocity, a light gate can give an average speed over a very small length of time.

HW Single sheet exam question.

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Heisenberg is out for a drive when he's stopped by a traffic cop. The cop says 'Do you know how fast you were going?' Heisenberg says 'No, but I know where I am.'

08/09/05 J6

We sorted out who was in the class and books were issued. We'll be covering PHY1 Mechanics and Radioactivity in our lessons. We started the small measurement topic by looking at how Vernier callipers work and talking about errors.

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Q: How does the barber cut the moon's hair? A: Eclipse it.