Question

Suppose you needed to raise a\(250\;{\rm{kg}}\)mower a distance of\(6.0\;{\rm{cm}}\)above the ground to change a tire. If you had a\(2.0\;{\rm{m}}\)long lever, where would you place the fulcrum if your force was limited to\(300\;{\rm{N}}\)?

Short answer

The fulcrum should be at a distance of\(1.78\;{\rm{m}}\).

Step-by-step solution

Given Data 

The load is\(W = 250\;{\rm{kg}}\).

The distance moved by the load is \(d = 6\;{\rm{cm}}\).

The lever arm is\(l = 2.0\;{\rm{m}}\)

Calculation of the force

Let, the fulcrum is at a distance r from the point of load.

The torque by the forces is zero at equilibrium. So,

\(\begin{align}\sum \tau &= 0\\300 \times r &= 250 \times 9.8\left( {2 - r} \right)\\\left( {300 + 2450} \right)r &= 2450 \times 2\\r &= 1.78\;m\end{align}\)

The fulcrum should be at a distance of\(1.78\;{\rm{m}}\).