Matter and Motion

This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1876 edition. Excerpt: ...Hence = i (V'+V). (2) Multiplying the corresponding members of equations (1) and (2) each by each wo obtain--FS = J MV-iMV (8) Here F S is the work done by the force F acting on the body while it moves through the space 8 in the direction of the force, and this is equal to the excess of i MY'2 above MV2. If we call i MV2, or half the product of the mass, into the square of the velocity, the kinetic energy of the body at first, then MV'2 will be the kinetic energy after the action of the force F through the space S. The energy is here expressed in footpoundals. We may now express the equation in words by saying that the work done by the force ¥ in changing the motion of the body is measured by the. increase of the kinetic energy of the body during the time that the force acts. We have proved that this is true when the interval of time is so small that we may consider the force as constant during that time, and the mean velocity during the interval as the arithmetical mean of the velocities at the beginning and end of the interval. This assumption, which is exactly true when the force is constant, however long the interval may be, becomes in every case more and more nearly true as the interval of time taken becomes smaller and smaller. By dividing the whole time of action into small parts, and proving that in each of these the work done is equal to the increase of the kinetic energy of the body, we may, by adding the successive portions of the work and the successive increments of energy, arrive at the result that the total work done by the force is equal to the total increase of kinetic energy. If the force acts on the body in the direction opposite to its motion, the kinetic energy of the body will bo diminished instead of being...