Conversations on Natural Philosophy, in which the Elements of that Science are Familiarly Explained

by Mrs. Marcet; Thomas P. Jones

Mrs. B. You comprehend then, that the extremity of the longest arm of a lever, must move with greater velocity than that of the shortest arm, and that its momentum is greater in proportion.

Emily. No doubt, because it is farthest from the centre of motion. And pray, Mrs. B., when my brothers play at see-saw, is not the plank on which they ride, a kind of lever?

Mrs. B. Certainly; the log of wood which supports it from the ground is the fulcrum, and those who ride, represent the power and the resistance at the ends of the lever. And have you not observed that when those who ride are of equal weight, the plank must be supported in the middle, to make the two arms equal; whilst if the persons differ in weight, the plank must be drawn a little farther over the prop, to make the arms unequal, and the lightest person, who may be supposed to represent the power, must be placed at the extremity of the longest arm.

Caroline. That is always the case when I ride on a plank with my youngest brother; I have observed also that the lightest person has the best ride, as he moves both further and quicker; and I now understand that it is because he is more distant from the centre of motion.

Mrs. B. The greater velocity with which your little brother moves, renders his momentum equal to yours.

Caroline. Yes; I have the most weight, he the greatest velocity; so that upon the whole our momentums are equal. But you said, Mrs. B., that the power should be greater than the resistance, to put the machine in motion; how then can the plank move if the momentums of the persons who ride are equal?

Mrs. B. Because each person at his descent touches and pushes against the ground with his feet; the reaction of which gives him an impulse which produces the motion; this spring is requisite to destroy the equilibrium of the power and the resistance, otherwise the plank would not move. Did you ever observe that a lever describes the arc of a circle in its motion?

Emily. No; it appears to me to rise and descend perpendicularly; at least I always thought so.

Mrs. B. I believe I must make a sketch of you and your brother riding on a plank, in order to convince you of your error. ([fig. 4. plate 4.]) You may now observe that a lever can move only round the fulcrum, since that is the centre of motion; it would be impossible for you to rise perpendicularly, to the point A; or for your brother to descend in a straight line, to the point B; you must in rising, and he in descending, describe arcs of your respective circles. This drawing shows you also how much superior his velocity must be to yours; for if you could swing quite round, you would each complete your respective circles, in the same time.