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I am fairly familiar with physics. However I have a question regarding the math behind a lever mechanism. Why is it easier to exert force on something the longer the arm of the lever is? What is the math/equations behind this?

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- #1

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I am fairly familiar with physics. However I have a question regarding the math behind a lever mechanism. Why is it easier to exert force on something the longer the arm of the lever is? What is the math/equations behind this?

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The article describes the necessary mathematics behind this as well. Note that its not necessarily the length of the lever that produces the larger torque (on an actual lever however, the handle is undoubtedly at the end) but the larger distance from the pivot point.

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Doc Al

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Whatever torque is created by the weight of the box about the fulcrum is what you'll have to exert to lift the box. If you're pushing down at the end of the lever you'll have to exert a force equal to the weight of the box (or a bit more), since the fulcrum is in the middle.

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The same amount of torque must be exerted in the opposite direction to lift the box. The amount of force needed to generate the opposing torque is dependent on the location that force is applied. If applied at the opposing end, you'd only need to exert the same amount of force which is generated by the mass of the box. In this case since you've conveniently chosen 1 kg, you'd have to exert 9.81 N. However if you'd placed your force closer towards the fulcrum you'd have solve for the required force as governed by τ=Fd, where τ would be the amount of torque, F is your force, and d is your distance to the fulcrum.

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