Levers are a clever way of moving something heavy that you wouldn’t be able to move just by pushing on it. A lever consists of a “lever arm”, which is free to pivot about a point, or “fulcrum”. It relies on having the distance L1 be larger than L2. By pushing on the long arm, the force F1 you apply gets...
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Levers are a clever way of moving something heavy that you wouldn’t be able to move just by pushing on it. A lever consists of a “lever arm”, which is free to pivot about a point, or “fulcrum”. It relies on having the distance L1 be larger than L2. By pushing on the long arm, the force F1 you apply gets multiplied, and a much larger force F2 is applied to the load.
At first glance, it seems like you get “something for nothing” when using a lever; you apply a small force, and you’re able to move an object with a much larger force! On closer inspection, it turns out not to be so; the work done on the object matches exactly the work you put in. Here, we will derive the basic lever equation
F1/F2 = L2/L1
Part 1
If you push the long end of the lever down a distance d1, how much does the other end move up? (Call this distance d2.) Express you answer in terms of L1 and L2.
Part 2
Assume that the work you do is equal the work done on the load. Express this assumption in terms of the forces F1 and F2 and displacements d1 and d2, and use your answer from part 1 to derive the lever equation.
Part 3 (you can do this part without doing part 1 or 2)
If I gave you a lever arm 10 m long, where would you have to rest it on the fulcrum to lift a 1000 kg object off the ground? (I.e., what must the ratio L1/L2 be?) (Hint: The force you can exert is probably largest if you lean on it and push down with all your weight.)
7 answers
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2 days ago