Chapter 6, Problem 8P

A lever such as that shown in Fig. 6-35 can be used to lift objects we might not otherwise be able to lift. Show that the ratio of output force, F_o, to input force, F₁, is related to the lengths l₁and l_ofrom the pivot by F_o/F₁, = I₁/I_o. Ignore friction and the mass of the lever, and assume the work output equals the work input.

Figure 6-35

To determine

The ratio of output force to input force is equal to the ratio of the input length to output length.

Answer to Problem 8P

Solution:The ratio of output force to input force is equal to the ratio of the input length to output length. i.e. $\frac{F_o}{F_I}=\frac{l_I}{l_o}$ .

Explanation of Solution

The turning effect produced by input force must be equal to turning effect produced by output force. This turning effect can be measured by measuring the moment of force.

Hence, turning effect produced by input force = turning effect produced by output force.

  $\Rightarrow$ $F_o{l}_o=F_I{l}_I$

  $\therefore \frac{F_o}{F_I}=\frac{l_I}{l_o}$

Conclusion:The ratio of output force to input force is equal to the ratio of the input length to output length. i.e. $\frac{F_o}{F_I}=\frac{l_I}{l_o}$ .