An object of mass m initially at rest on a smooth horizontal plane starts moving under the action of force F = 2N . In the process of its linear motion, the angle θ (as shown in figure) between the direction of force

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An object of mass m initially at rest on a smooth horizontal plane starts moving under the action of force F = 2N . In

As seen in the free body diagram of the object, normal force $N$ , weight $mg$ and force in parallel and perpendicular directions are acting.

Using Newton's law of motion

Along horizontal direction, $Fcos\theta = ma$

$⇒ 2\cos ( kx ) = mv\dfrac{d v}{d x}$

Integrating the above relation, we have

${∫}_{0}^{v}v d v = 2{∫}_{0}^{x}\cos ( kx ) d x$

$⇒ \dfrac{m{v}^{2}}{2} = \dfrac{2}{k}sinkx$

Thus, kinetic energy of the object will be $K . E . = \dfrac{2}{k}sin\theta$

Thus, the value of $n = 2$ .

An object of mass m initially at rest on a smooth horizontal plane...

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