Math  /  Algebra

Question(II) A lever such as that shown in Fig. 7-20 can be used to lift objects we might not otherwise be able to lift. Show that the ratio of output force, FOF_{\mathrm{O}}, to input force, FIF_{\mathrm{I}}, is related to the lengths I\ell_{\mathrm{I}} and O\ell_{\mathrm{O}} from the pivot by FO/FI=I/OF_{\mathrm{O}} / F_{\mathrm{I}}=\ell_{\mathrm{I}} / \ell_{\mathrm{O}}. Ignore friction and the mass of the lever, and assume the work output equals the work input. (a)
FIGURE 7-20 A lever. Problem 11. (b)

Studdy Solution
Solve for the ratio of forces.
Set the torques equal to each other:
FI×I=FO×O F_{\mathrm{I}} \times \ell_{\mathrm{I}} = F_{\mathrm{O}} \times \ell_{\mathrm{O}}
Rearrange to find the ratio of forces:
FOFI=IO \frac{F_{\mathrm{O}}}{F_{\mathrm{I}}} = \frac{\ell_{\mathrm{I}}}{\ell_{\mathrm{O}}}
This shows that the ratio of the output force to the input force is equal to the ratio of the lengths from the pivot.

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