Chapter 6, Problem 57P

How long will It take a 2750-W motor to lift a 385-kg piano to a sixth-story window 16.0 m above?

To determine

The time it takes for a $\text{2750}\text{watt}$ motor to lift a $\text{ 385}\text{kg}$ piano sixth story window $\text{16}\text{.0}\text{m}$ above.

Answer to Problem 57P

Solution:

  $\text{22 s}$

Explanation of Solution

Given:

Power of motor, $P\text{=}\text{2750}\text{W}$

Mass of piano, $m\text{=}\text{385}\text{kg}$

Vertical displacement, $h\text{=16}\text{.0}\text{m}$

Formula used:

Power= $\frac{\text{work}}{\text{time}}$

Work done: Applied force $\times$ Displacement

Calculation:

Work done in lifting the piano

  $\begin{array}{l}W={\overrightarrow{F}}_p\cdot \overrightarrow{S}\\ =F_{P}S\text{cos}{0}^0\\ =F_{P}S\end{array}$

From Newton’s second law:

  $F_p=mg$

  $\begin{array}{l}\text{=}mgs\\ \text{=}\text{385}\text{kg×9}\text{.80}{\text{m/s}}^{\text{2}}\text{×16}\text{.0}\text{m}\\ \text{= 60368}\text{J}\end{array}$

  $\begin{array}{l}\text{time=}\frac{\text{work}}{\text{power}}\\ \text{=}\frac{\text{60368}\text{J}}{\text{2750}\text{J/s}}\\ =21.952\text{s}\\ =22\text{s}\end{array}$

Conclusion:

The time it takes for a $\text{2750}\text{watt}$ motor to lift a $\text{ 385}\text{kg}$ piano sixth story window $\text{16}\text{.0}\text{m}$ above $\text{22 s}$ .