Question

A 3kg box is pushed with a force of 15 N across a friction less floor for 3 second.
What is the power exerted on the box?

Answer 1

QUESTION:

A 3kg box is pushed with a force of 15 N across a friction less floor for 3 second. What is the power exerted on the box?

SOLUTION:

Power is

$$P = \frac {W}{t}$$

Where work $W = F \cdot s$

As floor is frictionless:

$$F = m \cdot a$$ $$a = \frac {F}{m}$$ $$s = \frac {at^2}{2} = \frac {Ft^2}{2m}$$

Hence

$$W = F \cdot s$$ $$W = \frac {F^2 t^2}{2m}$$

And power

$$P = \frac {W}{t} = \frac {\frac {F^2 t^2}{2m}}{t} = \frac {F^2 t}{2m}$$ $$P = \frac {15^2 \cdot 3}{2 \cdot 3} = 112.5 \text{ W}$$

Another way:

According to the work-energy theorem, in this case

$$W = \frac {m v^2}{2}$$ $$v = at$$ $$F = ma$$ $$a = \frac {F}{m}$$ $$v = \frac {Ft}{m}, \text{ hence}$$ $$W = \frac {mv^2}{2} = \frac {m}{2} \left(\frac {Ft}{m}\right)^2 = \frac {m F^2 t^2}{2m^2} = \frac {F^2 t^2}{2m}$$

And power

$$P = \frac {W}{t} = \frac {\frac {F^2 t^2}{2m}}{t} = \frac {F^2 t}{2m}$$ $$P = \frac {15^2 \cdot 3}{2 \cdot 3} = 112.5 \text{ W}$$