. Theory of the relativity of motion . X Dynamics of a Particle. 75 Let it be accelerated in the X direction by the action of the com-ponent forces Fx and Fy. From our general equation (59) for the force acting on a particlewe have for these component forces Fx =. (64) (65) Introducing the condition that all the acceleration is to be in the Y dudirection, which makes -—■ = 0, and further noting that u2 by the division of equation (64) by (65), we obtain Hi x I Uy ) FyFx = uxu XWy C£ ~ Ux & _ u. Fv. (66) Hence, in order to accelerate a particle in a given direction, we mayapply any force Fy in
. Theory of the relativity of motion . X Dynamics of a Particle. 75 Let it be accelerated in the X direction by the action of the com-ponent forces Fx and Fy. From our general equation (59) for the force acting on a particlewe have for these component forces Fx =. (64) (65) Introducing the condition that all the acceleration is to be in the Y dudirection, which makes -—■ = 0, and further noting that u2 by the division of equation (64) by (65), we obtain Hi x I Uy ) FyFx = uxu XWy C£ ~ Ux & _ u. Fv. (66) Hence, in order to accelerate a particle in a given direction, we mayapply any force Fy in the desired direction, but must at the same timeapply at right angles another force Fx whose magnitude is given byequation (66). Although at first sight this state of affairs might seem ratherunexpected, a simple qualitative consideration will show the necessityof a component of force perpendicular to the desired again to figure 12; since the particle is being accelerated in the Ydirection, its total velocity and hence its mass are increasing. Thisincreasing mass is accompanied by increasing momentum in the Xdirection even when the velocity in that direction remains component force Fx is necessary for the production
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