# Thread: I don't understand how a lever works

1. Ok, I'm not a physics major and I'm reading 'the way things work' by macaulay and it says that if you have a mammoth on one end of a lever and 9 people on the other side lifting it, and then you move the fulcrum 3x closer to the load that you would only need a third of the people to lift the mammoth. At face value it seems fine, but when I try to think about it logically I just don't understand how doing that would make it so much easier to lift the weight. Can someone please explain in layman's terms how moving a fulcrum 3x closer to a load for say a 10,000 pound object can shed almost 7,000 lbs off the weight?

2.

3. Levers are simply a matter of ratios.

Imagine a lever with 10kg on one end and a fulcrum in the exact centre:

??___________________________10
---jjthe ehw---------^
The length of the left side to the length of the right side is a ratio of 1:1.
Therefore it will take 10kg to lift the 10kg.

But then imagine a lever with 10kg on one end and a fulcrum at the 2/3 point:

??___________________________10
-----------rhe-jjj-------j -----^

The ratio of lengths is now 2:1.
Therefore it will take 5kg to lift the 10kg weight.

It is all to do with where the fulcrum is; the ratio of the left side to the right side.
So if it takes 9 people to lift a mammoth when the fulcrum is in the centre (1:1), then the fulcrum would need to be at the 3/4 mark (3:1) for 3 people to lift the mammoth.

If it helps: find a wooden stick, a weight and a pencil. Use the pencil as the fulcrum and move it left and right to feel the effect it has on how heavy the weight feels.
(It's early - I hope that makes sense.)

4. Torque is the important idea in this situation. It is the tendency of a force to turn an object about an axis. In this case, the object is a plank with an elephant on it and the axis is the fulcrum. The magnitude of the torque is given by d x F, where F is the force applied to the object and d is the distance from the axis to the thing applying the force.
So, if you have a 20m plank with the fulcrum right in the middle, and a 1000kg elephant sitting on one end, the weight of the elephant will be applying (10m)x(1000kg x 10m/s2) = 100000Nm of torque to the system. In order to lift the elephant, you need to apply more than 100000Nm of torque to the other end of the plank. To match that, you'll need to apply (100000Nm)/(10m) = 10000N of force to the other end of the plank.
Now, if you move the fulcrum so that the elephant is only 2m away from it, the elephant is now only applying (2m)x(1000kg x 10m/s2) = 20000Nm of torque to the system. Even better, you only need to apply (20000Nm)/(18m) = 1111.11N of force to the other end of the plank to match it.

5. Have you ever watched kids playing on a teeter-totter?
The smaller kids sit closer to the end of the plank than the big kids do so they can balance each other.

6. Originally Posted by curious_
Ok, I'm not a physics major and I'm reading 'the way things work' by macaulay and it says that if you have a mammoth on one end of a lever and 9 people on the other side lifting it, and then you move the fulcrum 3x closer to the load that you would only need a third of the people to lift the mammoth. At face value it seems fine, but when I try to think about it logically I just don't understand how doing that would make it so much easier to lift the weight. Can someone please explain in layman's terms how moving a fulcrum 3x closer to a load for say a 10,000 pound object can shed almost 7,000 lbs off the weight?
It should be noted that while moving the fulcrum 3x closer allows the load to be lifted with only a third of the force, the load can only be lifted a third of the distance. Thus, it requires the same amount of work to lift the load regardless of where the fulcrum is.

7. Lever, gear, and even transformer action is a game of ratio. One gains power advantage, but must sacrifice motivational advantage. You can lift twice the weight, but you will need to move twice as far.

8. Basically, you're trading force for distance in that type of lever. But it's not a free lunch.

You still have the expend the same amount of energy,but it's over a longer distance. If you think of a lever as a teeter-totter, and you move the fulcrum closer to the fat kid, the skinny kid will go up and down a greater distance than the fat kid, but they will nearly balance each other's weight.

9. Thank you all for your replies As a layman, it's hard for me to explain why I don't understand the physics behind this concept but I will try. The balancing of the see-saw makes sense to me, and also the fact that if you had to move something a longer distance it would require more work, but I just don't understand why moving the fulcrum 3x closer to the load allows 3 people instead of 9 to be able to lift it. What is it about the fulcrum that makes the load so much lighter? Like if 12 people could pick a car up off of the ground 3 ft in distance without any lever, and then 4 people tried to lift it 1 foot, they wouldn't be able to do it because its just too heavy. Or as a more extreme example say 1,000 people were able to pick up a small airplane and they could get it 3 ft off the ground. If you lower the number to 333 people I don't think they'd be able to lift it a third of the distance (not even an inch off the ground). So I just don't understand how introducing a lever/fulcrum changes this fact. :/

10. A lever works because it's an application of force x distance.
1/3 the force at 3 times the distance is exactly the same as 1 x force at 1 x the distance.
In your example of 1000 people vs 333 the distance (that the force is applied over) is the same in both cases - in this case it's being applied directly, hence they wouldn't (for the sake of argument) be able to lift it a third of the height.

11. Originally Posted by curious_
If you lower the number to 333 people I don't think they'd be able to lift it a third of the distance (not even an inch off the ground). So I just don't understand how introducing a lever/fulcrum changes this fact. :/
Do you think a man can lift a car with a hydraulic jack? You know he can, don't you? Then why would you doubt that 333 people can lift an airplane with a lever?

12. The key is the distance that the weight is being moved. The 3 people who are lifting the elephant have to move their end of the lever 3 times as far as the 9 people did to effect the same amount of lift on the elephant. It is like this with all simple machines. They all trade distance for power.

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