Abstract
IT is commonly said that change of momentum is evidence that force has acted or is acting on the mass, and that the rate at which the momentum is changing is the measure of the force. Thus, in his lecture on “Force,” Prof. Tait says: “Force is the rate of change of momentum” (NATURE, vol. xiv. p. 462). This is not true if the mass be variable. Suppose a sphere of ice moving with constant velocity in a straight line through hot space. The mass, and therefore the momentum, is changing at every instant by the evaporation of the ice. The evaporation being supposed uniform over the entire surface, any force impressed on the sphere by the mutual repulsion between it and a particle of vapour thrown off at a point, p, is balanced by an equal force at the other end of the diameter through p. Hence, the resultant of all these forces is nothing. Here, then, we have change of momentum of the sphere, although no force acts on it. In like manner the change of momentum of a rocket and of a locomotive engine is partly due to change of mass. Does it not hence appear that change of velocity is the proper evidence of the action of force? When a variable mass, m, is in motion, the proper measure of the force acting on m at any given instant in any given direction is—not the rate of change of momentum, but—the product of the value of the mass at that instant, and the value of the rate of change of the velocity at that instant and in that direction, i.e., the measure of the force is not d(mv)/dt but mdv/dt
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G., E. Force and Momentum. Nature 21, 108 (1879). https://doi.org/10.1038/021108a0
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DOI: https://doi.org/10.1038/021108a0
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