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 Relation between the Components of Force Parallel and Perpendicular to the Acceleration.



Consider a body (fig. 1) moving with the velocity

$\mathsf{u}=u_{x}\mathsf{i}+u_{y}\mathsf{j}.$

Let it be accelerated in the Y direction by the action of the component forces $$\mathsf{F}_{y}$$ and $$\mathsf{F}_{x}$$.

From equation (2) we have

Introducing the condition that there is no acceleration in the X direction, which makes $$du_{x}/dt=0$$, further noting that $$u^{2}=u_{x}^{2}+u_{y}^{2}$$, by the division of equation (3) by (4) we obtain

Hence in order to accelerate a body in a given direction, we may apply any force $$\mathsf{F}_{y}$$ in the desired direction, but must at the same time apply at right angles another force $$\mathsf{F}_{x}$$ whose magnitude is given by equation (5).

From a qualitative consideration, it is also possible to see the necessity of a component of force, perpendicular to the