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A Classless System

“Or as my dad always says, 'It only becomes a social problem when the working man joins in.'” - Ben Aaronovitch, Lies Sleeping

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If you want 200 kg blocks moved about… then Stuart is your man

Stupidity

Some people think that stupidity has risen with the internet. However it existed well before that.

Look in virtually any A-Level text book or any fitness book (or look online, e.g. here) and you will see the following diagram using the calf raise as an example of a 2nd class lever and comparing it to a wheelbarrow:

Fig 1 - According to the texts this an example of a 2nd class lever. If the bodyweight of the person is 600 Newtons this is taken to be the load on the ankle. The pivot is taken to be the ball of the foot. Thus the force exerted by the muscle is calculated in the above example to be 400 N, i.e. muscle tension is calculated to be less than bodyweight.

Yet something about it doesn't quite make sense... because if you turn it over so that the person performs a calf press with a weigh equal to his bodyweight of 600 Newtons (e.g. on a vertical leg press machine) it becomes a 1st class lever - so the forces come out different when obviously they shouldn't, i.e. muscle tension is now calculated to be 1200 N which is twice the bodyweight of 600 N:

Fig 2 - As a 1st class lever the pivot is taken to be the ankle, the load of 600 N is on the ball of the foot thus the calf force is calculated to be 1200 N.

The reason for this discrepancy in calf forces between the 2nd and 1st class levers is that the load on the ankle joint is not bodyweight - the load on the ankle is instead bodyweight + calf muscle tension.

Newton's 3rd Law

It is much better to avoid using the 3 class system of levers and instead bear in mind Newton's 3rd Law:

Fig 3 - The 3rd Law states that for every action there must be an equal and opposite reaction. Thus when it comes to levers all opposing forces must balance AND all moments must balance. Note that I have turned this diagram on its side because an alarming amount of people get confused by the the ups and downs and thus assign efforts, loads and pivots to levers... when in fact all points are points of force and all points are pivots. Note that this style of diagram also works if more points are added as in a 4, 5, 6 points or more levers.

Thus a 3 point lever should obey the following:

Opposing Forces

F1 + F2 = F3

Opposing Moments

F1l1 = F2l2

F3l1 = F2l3

F3l2 = F1l3

Also of course l1 + l2 = l3.

The terrible 3 class system of levers arbitrarily places where the pivot is and by convention ignores this as an opposing force... so it is best to avoid the 3 class system of levers and instead make sure that all opposing forces balance and all moments balance, i.e. use the classless system in Fig 3.

Here is one way of envisioning the classless system;

Fig 4 - In this diagram the cars push against a bar. None of the cars has a special vaunted role of being the pivot. Using the 3 class system and assigning a pivot and therefore ignoring the pivot as a source of force leads to the potential for calculation errors. By turning the diagram on its side and using these cars I hope to illustrate the absurdity of thinking of a 'fixed', 'forceless' pivot.

Do not think of the 3 class system or of pivots but use Newton's 3rd Law and thus Fig 3 or 4 above, so the diagram of the calf should look like this:

Fig 5 - The load on the ball of the foot is obviously the weight of the person (600 N) and if the horizontal pivot points are 20 cm and 10 cm, this means that the calf force is 1200 N. Thus the total force on the ankle joint is 1800 N - this is because the calf muscle attaches to the tibia thus compressing it into the ankle with 1200 N of force which added to the 600 N bodyweight totals 1800 N. Thus all opposing forces balance and all torques balance.

Conclusion

The only way the calf, in the traditional 3 class system, would operate as a 2nd class lever in wheelbarrow mode is if the calf muscle at it's upper end were attached to an external object. A wheelbarrow is a 2nd class lever because the person lifting the wheelbarrow is external to the wheelbarrow. A calf is 1st class lever because the muscle is attached to its own lifting system, it is not attached to an external system.

The fact is that any 3 point lever can be considered as either a 1st, 2nd or 3rd class lever and hence the 3 class system of levers is useless - all levers are in fact classless; Figs 3, 4 and 5 should always be used.

11th October 2023