9.5 Simple machines  (Page 2/4)

In the case of the wheelbarrow, the output force or load is between the pivot (the wheel’s axle) and the input or applied force. In the case of the shovel, the input force is between the pivot (at the end of the handle) and the load, but the input lever arm is shorter than the output lever arm. In this case, the MA is less than one.

Another very simple machine is the inclined plane. Pushing a cart up a plane is easier than lifting the same cart straight up to the top using a ladder, because the applied force is less. However, the work done in both cases (assuming the work done by friction is negligible) is the same. Inclined lanes or ramps were probably used during the construction of the Egyptian pyramids to move large blocks of stone to the top.

A crank is a lever that can be rotated $\text{360º}$ about its pivot, as shown in [link] . Such a machine may not look like a lever, but the physics of its actions remain the same. The MA for a crank is simply the ratio of the radii $r_{\text{i}}/r_0$ . Wheels and gears have this simple expression for their MAs too. The MA can be greater than 1, as it is for the crank, or less than 1, as it is for the simplified car axle driving the wheels, as shown. If the axle’s radius is $\mathrm{2.0\; cm}$ and the wheel’s radius is $\text{24.0 cm}$ , then $\text{MA}=2.0/\text{24.0}=0\text{.}\text{083}$ and the axle would have to exert a force of $\text{12,000 N}$ on the wheel to enable it to exert a force of $\text{1000 N}$ on the ground.