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Question

A constant force of $$2.50\ N$$ accelerates a stationary particle of mass $$15\ g$$ through a displacement of $$2.50\ m$$. Find the work done and the average power delivered.


Solution

Given that

Force $$F = 2.5\ N$$.

Mass of the particle $$m = 15\ g =0.015\ kg$$

Displacement covered by the particles $$s = 2.5\ m$$.


Now, For Work,

Work Done = Force × Displacement

 $$ W=2.5\times 2.5 $$

 $$ W=6.25\,J $$

Hence, the Work done by the Particles is $$6.25\ J$$.


Now, For Power,

Work Done = $$6.25\ J$$.

Initial Velocity $$u = 0$$

Using Newton's second law of Motion,

  $$ F=ma $$

 $$ a=\dfrac{m}{F} $$

 $$ a=\dfrac{2.5}{0.015} $$

 $$ a=166.67\,m/{{s}^{2}} $$

 Now, the time taken for the displacement is:

$$s=ut+\dfrac12at^2$$

$$2.5=0+\dfrac12\times\dfrac{500}{3}\times t^2$$

$$t=\sqrt{\dfrac{5\times3}{500}}=0.1\sqrt3$$


Now, Power = Work/Time.

  $$ P=\dfrac{W}{t} $$

 $$ P=\dfrac{6.25}{0.1\sqrt{3}} $$

 $$ P=36.08\,W $$

Hence, the work done is $$6.25 J$$ and power is $$36.08 W$$


Physics

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