Like if you take a wrench and attach a long pipe to it so you can more easily turn whatever the wrench is holding. I just have trouble understanding how making the ‘arm’ longer increases the force on the pivot without you having to push any harder on the end of the arm.
In: Physics
The work you do is a function of the force you apply and the distance you travel
When you use a wrench or similar, you are ultimately making a circular path with the force being applied perpendicular to the lever arm
If you trace out your circular trajectory, measure how long that arc is, and multiply it by the force applied, you end up with the total work done.
As you make the lever arm longer, the arc length gets longer as well. If you have a further distance, you need less force to achieve the same work.
The moment of force on the object you are trying to turn is a combination of force applied to the lever (let’s use the end of the level in this example to make it easier), and the force you put on the end of the lever. [For completeness, the equation is M = rF (‘r’ being distance from object, ‘F’ being force applied to lever)]
Imagine you only have a lever of one length to begin with. The only way you can try to turn the object with more force is by pushing harder on the end of the lever. This is increasing the ‘force’.
But you could increase the length of the lever instead and keep your push force the same. This would turn the object with more moment force, by only increasing the ‘distance’.
Work is force times distance. If you have a long lever, you can apply a small force on it, but since you move it a long distance it still turns into a lot of work. On the other end of the lever the same work is active, but since the distance is much shorter, the force needs to be much higher.
Now with levers it is all a bit more complicated, so we don’t call it work but rather torque, but it is basically the same principle.
The best relationship I can thing of is pushing a door. If you push very close to the hinge you can still open the door, however it takes quite a bit of strength. On the other hand if you push nearer to the latch of the door you need lessor strength than that of pushing close to the hinge. The pivot point in the door is the hinge. So going a bit deeper giving you simple numbers thing of it this way. You have 10lbs of force, and the distance to the pivot is 10 inches. Its a simple multiplication you now have 100 inch-lbs of torque. Extend that distance to 20 inches with the same force (10 lbs) and you have 200 inch-lbs of torque. Literally doubling the strength by only increasing the distance. This works in the opposite direction as well. Keep the 10 inch distance with 20 lbs force you will have 200 inch-lbs of torque.
Another good example of this is a see saw where there are two unequal weighted children. You can balance them by adjusting the distance from the point of rotation (or fulcrum)
I hope this provides clarity. I’m happy to explain more if you need.
Torque!
Work = Force * Distance
Longer lever arm (long pipe in your example) increases distance. This means less force needed for the same amount of work.
Note: I am *not* a physics guy—someone more qualified please help out if this is wrong! I’m sure there’s something I may have missed in the explanation.
It is like gearing down a car, with a gear you spin it more to produce less forward motion allowing more torque but lower speed. With a really long lever, it is the same thing. The amount of distance traveled by the levered end is lowered while the distance traveled by the end you are articulating goes up. You can measure this by strapping a load to an end of the lever and measuring its vertical distance depending on where the fulcrum is placed. The further the fulcrum from you, the lever operator, the lower the effort but less vertical distance that load will climb.
So if you need to lift a load three centimeters, the end of your lever can be quite far away from the fulcum such that a small child could articulate it. There is a demonstration of this principle in the Boston Science Museum.
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