h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

This one is bugging me. I should know this as I aced in Physics many years ago. However.

Can somebody explain why it is that objects appear to get heavier with increasing distance from a pivot point? If I hold a 10kg weight above my head it feels lighter than holding it at arms length horizontally away from me. The force on the object in both situations is 10g Newtons, however the forces on me are greater in the second situation than the first.

CR

There must be many ways of answering this. Here's a couple.

If you are pressing the lever one meter from the pivot, and the weight is two meters away, then the weight will move twice as far as your hand.

Energy = Force * Distance moved, so by conservation of energy, as you are only putting in half the distance moved, you have to put in twice the force to make up for it.

Alternatively, you can think about it using Force = Mass * Acceleration. The weight will be moving (accelerating) twice as fast as your hand, so it seems like you are accellerating a 20 N weight at the same speed as your hand, when really you are accelerating a 10 N weight at twice the speed of your hand - your hand can't tell the difference, as it needs the same force to do both.

Basically, levers allow you to swap force for distance (and speed): you can use a larger force to get something to move more quickly, (like flicking a bogey off a ruler) or a smaller force, which means you have to move your arm a longer distance.

Thanks for the reply!

After asking the question I resolved it this way : The definition of Work (or Energy expended) is Force * Distance. The same amount of Work is expended moving the weight through a fixed angle irrespective of where you apply the force. If you apply the force close to the weight, you have to move through a large angle, and thus the distance is greater. If you apply the force close to the pivot point, the angle that the force moves through is considerably smaller. However because the Work expended must be exactly the same in both cases, the forces required are different. Because the angle of movement and the distance to the pivot point are directly proportional to each other, the law of the lever can be deduced.

I think we are saying the same thing.

Now that I am many years removed from my schooling, I have realised that a lot of what I learned in physics were just rote formulas that I accepted without really understanding. For example, even after graduating with honours in Electrical Engineering, I can't really explain to you very well how electricity works. It probably explains why I didn't pursue electronics as a career! I just would like to be in a position of better understanding, so that I can explain it to others without making it seem dead and difficult to comprehend.

CR

So what exactly is a "moment"? Is it just the force * displacement formula applied to angles? Say, it requires a force of 1N to move a mass of 1kg at the end of a rod 1m long through 1 radian? Or 1 steradian? Or am I spouting total nonsense?

Pete, you have identified one of the problems of physics - the use of terminology that may have made sense some centuries ago, but now seem a bit cumbersome to us today. Another example is "lines of magnetic force" to describe magnetism.

I like to think of a moment as an "apparent turning force" relative to a fixed reference point around which an object resolves. A force of 1N, 1 metre away has the same effect at the central point as a force of 2N, 50 centimetres away, and both "moments" cancel each other out if they act in opposite directions to each other.

"Apparently Mechanical" Woodpigeon

Like the way that conventional current is in the opposite direction to the flow of electrons? Or that the Earth's "magnetic north pole" is really a south pole?

These anomalies exist for purely hysterical raisins (historical reasons).

srry if this has already been said, i didnt read all the backlog, but when u hold it obove ur head, u have your intire body underneath ur arm to hold u up, but when u hold it infront of u, its only ur arm holding it up, with no other support.