Question

A crowbar of length 2.0 m is used as a machine, to lift a box of 100 kgf by placing a fulcrum at a distance of 0.1 m from the box, calculate (i) the velocity ratio (ii) effort required. What assumption has been made in solving the problem ?

Answer 1

Dear Student,

$$\begin{gathered} \mathrm{Length}\mathrm{of}\mathrm{crow}\mathrm{bar}=2\mathrm{m} \\ \mathrm{length}\mathrm{of}\mathrm{load}\mathrm{arm},\mathrm{d}=0.1\mathrm{m} \\ \mathrm{length}\mathrm{of}\mathrm{effort}\mathrm{arm},\mathrm{D}=2-0.1=1.9\mathrm{m} \\ \left(1\right)\mathrm{Velocity}\mathrm{ratio},\mathrm{VR}=\frac{\mathrm{D}}{\mathrm{d}} \\ \mathrm{VR}=\frac{1.9}{0.1}=19 \\ \left(2\right)\mathrm{mechanical}\mathrm{advantage},\mathrm{MA}=\frac{\mathrm{L}}{\mathrm{E}}=\mathrm{VR} \\ \frac{\mathrm{L}}{\mathrm{E}}=19 \\ \mathrm{E}=\frac{100}{19}=5.26\mathrm{kgf} \\ \mathrm{It}\mathrm{is}\mathrm{assumed}\mathrm{that}\mathrm{the}\mathrm{crow}\mathrm{bar}\mathrm{is}\mathrm{weightless}\mathrm{and}\mathrm{there}\mathrm{is}\mathrm{no}\mathrm{friction}\mathrm{at}\mathrm{the}\mathrm{fulcrum}. \end{gathered}$$