Page:Elementary Text-book of Physics (Anthony, 1897).djvu/61

 not equal to the one applied. Six mechanical powers are usually enumerated—the lever, pulley, wheel and axle, inclined plane, wedge, and screw.

(1) The Lever is any rigid_ bar, of which the weight may be neglected, resting on a fixed point called a fulcrum. From the proposition in § 40 it may be seen that if forces be applied to the ends of the lever there will be equilibrium when the resultant passes through the fulcrum, and the moments of force about the fulcrum are equal. Hence, if the forces act in parallel lines, it follows that the force at one end is to the force at the other end in the inverse ratio of the lengths of their respective lever-arms. If $$l$$ and $$l'$$ represent the lengths of the arms of the lever, and $$P$$ and $$P'$$ the forces applied to their respective extremities, then $$Pl = P'l'.$$

The principle of the equality of action and reaction enables us to substitute for the fulcrum a force equal to the resultant of the two forces. We have then a combination of forces as represented in the diagram (Fig. 16). Plainly, any one of these forces may be considered as taking the place of the fulcrum, and either of the others the power or the weight.

The lever is said to be of the first kind if $$R$$ is fulcrum and $$P$$ power, of the second kind if $$P'$$ is fulcrum and $$P$$ power, of the third kind if $$P$$ is fulcrum and $$R$$ power.

(2) The Pulley is a frictionless wheel, in the groove of which runs a perfectly flexible, inextensible cord. If the wheel be on a fixed axis, the pulley merely changes the direction of the force applied at one end of the cord. If the wheel be movable and one end of the cord fixed, and a force be applied to the other end parallel to the direction of the first part of the cord, the force acting on the pulley is double the force applied: for the stress on the cord gives rise to a force in each branch of it equal to the applied force; each of these forces acts on the wheel, and since the radii of the wheel are equal, the resultant of these two forces is a force equal to their sum applied at the centre of the