Force converter with axis of rotation
Over 2200 years ago, a clever Greek is said to have stated: ‘Give me a fixed point in space and I will unhinge the world’. Archimedes thus summarised the laws of leverage that we know today. Levers are force transducers. They enable us to exert a much greater force on the other side of the axis with a comparatively small force.
Levers in everyday life
We encounter levers all the time in everyday life: the seesaw in the playground, the wheelbarrow in the garden, the nutcracker at Christmas time - and the KNIPEX pliers in their various versions all year round. You don't need to have studied physics to visualise the effect of our own strength on a lever. Torques, vectors and angular velocities do play a role in deriving the formulae - but we have simplified the examples, as decimal places are not important in practice.
The one-sided lever
When looking at levers, there is a force arm, a load arm and a pivot point. In the case of a one-sided lever, the load arm and force arm are on the same line and the pivot point is at the end. The best example here is the wheelbarrow. We have loaded a steel rim with tyres weighing approx. 40kg, which acts downwards with a force F1 of 400N. The centre of the rim is 0.5m away from the axis of rotation/wheel (r1), the handles of the wheelbarrow on which I am lifting are 1.5m away from the axis of rotation/wheel (r2). If we neglect the weight of the wheelbarrow and the friction that occurs everywhere, it is easy to calculate the force with which I have to lift the wheelbarrow at the beginning.
If we derive the formula, the result is a simplified ratio of the two forces and the applied lengths:
-> Let's solve the equation according to F2: 
As we can see, the smaller the load arm r1 (i.e. the distance between the rim and the axle of the wheel) or the larger the force arm r2 (i.e. the length of the chassis up to the handle), the less force F2 I have to apply to lift the rim.
= 133,3N -> A force arm three times as long provides 1/3 of the force required, in our example this corresponds to a lift of only 13.3kg. For the very precise: This ratio is sliding for a wheelbarrow. The higher I lift the chassis, the more the ratio of r1 to r2 shifts. At some point, the force F1 acts directly on the axle, the load arm r1 is then 0cm long and I no longer have to apply any force at all. But it looks silly.
The two-sided lever
The same formula can also be applied to the two-sided lever. If you found yourself at the top of the seesaw because you were lighter than your opponent, you (perhaps successfully) slid further back and thus extended your power arm. Ha! The law of leverage can also be applied to pliers. The two long force arms moved by our muscle power increase the effect on the other side of the joint through shorter load arms.
So if, for example, the cutting surface of a diagonal cutter is very close to the joint, the load arm r1 is extremely short and the force F1 on the workpiece is correspondingly large. Let's take a look at our popular 74 02 160 high-leverage diagonal cutters: With an overall length of only 160 mm, the power arm is around 130 mm long, but if we cut close to the joint, the load arm is only 20 mm long. A normal hand pushes a diagonal cutter with a force of around 400N.
-> applied: 
= 2.600N!
Wow! That's a lot!
By way of comparison, let's take the larger 74 05 250 high-leverage diagonal cutter, designed for heavy-duty continuous use and therefore 250 mm long. Here the length of the power arm is around 210mm, the load arm again around 20mm.
-> angewendet: 
= 4.200N!
This is so much that piano wire with a diameter of up to 3 mm can be cut with this diagonal cutter without any effort.
Or let's take a pair of water pump pliers. Illustrated by our Cobra, the ratio looks like old familiar territory:
This time, if the force of our hands F2 is known, we solve the formula for the gripping force F1 if the jaws of the pliers are 50 mm long and the legs are 200 mm long.
-> applied: 
= 1.600N
We start from the tip of the jaws to hold a workpiece, for example. Closer to the joint, in the centre of the jaws for loosening or locking a nut, the force is even greater, as shown above.
Unhinging the earth
If you have now found the simple formula fun and want to get a bit silly, you can also ‘calculate’ how long the arm of force must be to unhinge the world. Perhaps we take the moon as the centre of rotation? The earth has a ‘weight’ of 5,972*1024kg and is on average 384,400km away from the moon (r1). Hang on to the force arm with your own weight, say 100kg (i.e. F2=100N)? Well? Physically speaking, this is of course nonsense.
With various further developments, the force can be multiplied, for example with a double joint like a bolt cutter. Here, the further distance that the
that the force arms have to be brought together in order to apply a large force on the load side over a short distance. Every pair of pliers has natural limits, such as the amount of force a person can apply with their hands or the span of their own fingers. KNIPEX has therefore been researching every day for decades to perfect its tools so that you will still be able to grip powerfully tomorrow.
P.S.: The lever in the task with the Earth would have to be 22,963,680,000,000,000,000,000,000,000,000,000 kilometres long.
