Yarnell's World of Math

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unique visitors since March 2009

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M1: Statics

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Don't worry, Mechanics fans, this is statics - not statistics.

Static means not changing. In particular we shall look at why a particle's position doesn't change. There is one key law that tells us the answer and it's called Newton's Law.

An object's motion dunt change unless summat meks it

Translated into modern English, this means that if the forces balance there is no reason why the motion should change. So if the forces are in equilibrium we have a static situation.

Types of Force

There are a few types of force we shall encounter.

• Weight. This is caused by gravity and (on Earth) is about 9.8 × mass. Weight always acts downwards.
• Tension. This is the force provided by a string. Yarnell's Rule for tensions is simple: one tension is needed per string. The direction of the force is always away from the particle.
• Normal Reaction. This is the force that stops something falling through a table or floor. It always acts normally ( at right angles) to the contact point.
• Pushes & Pulls are other forces that might be present.
• Friction. This cheeky little force can be anything from zero to a maximum value that depends on something called the coefficient of friction. Friction always does its best to oppose motion.

Friction

Friction is different to the other forces because it is not a fixed value. If a snooker ball is placed carefully on an smooth ice rink then it shouldn't move. This is because no friction is needed to hold it.

Now place a shoe on a table. If the table top is horizontal then no friction is needed, so F = 0.

But raise the table so it slopes and friction is necessary to stop the shoe sliding. A snooker ball would now begin to slide because it has a lot less friction than a shoe. As we increase the angle the table slopes at, more and more friction is needed to prevent the shoe sliding. Friction is increasing all the time until... finally at a certain angle the shoe starts to slide. Friction has lost the battle.

In reality friction has reached its maximum value and will continue to try its hardest to slow the shoe's slide down the slope. The maximum possible amount of friction depends on the coefficient of friction, a mysterious value that gets the symbol μ and is different for different materials. A rubber-soled shoe will have a much higher coefficient of friction than a snooker ball.

In fact, the maximum possible amount of friction is found by multiplying the coefficient of friction by the normal reaction.

F_max = μR

You can find the coefficient of friction for your shoe/table combination using only a protractor. Here's how. Place the shoe on the flat table. Now very slowly raise the slope. Very slowly. Keep going. A bit more. Slowly raising the slope until... the shoe slides. Hold the table at this angle and get a pal (I forgot to tell you that you'd need a helper) to measure the angle, θ, that the slope is making with the horizontal. To find μ use the equation μ = tan θ.

All statics questions are pretty much the same. Resolve forces in two (perpendicular) directions to get two equations. Usually you will need to solve simpletaneous equations. The two directions might be horizontal/vertical but when there is a slope it is easier to resolve parallel/perpendicular to the plane. Both ways are shown in the following clips. The exams needed are Jan 2001, Jan 2010 and (I think) June 2005 or maybe Jan 2006 or summat like that. I would find out but the wife's just come back from the bingo and I've still got the washing-up to do.