Question

A machine is driven by a $100\mathrm{kg}$ mass that falls $8\mathrm{m}$ on $4$ seconds. If the efficiency of the machine is $75\%$, what is the power output?

• A. $2000\mathrm{W}$
• B. $1000\mathrm{W}$
• C. $9202.2\mathrm{W}$
• D. $150\mathrm{W}$

Answer 1

The correct option is C

$9202.2\mathrm{W}$

Step 1: Given data

Mass $\left(\mathrm{m}\right)=100\mathrm{kg}$

Height $\left(\mathrm{h}\right)=8\mathrm{m}$

Efficiency $\left(\eta \right)=75\%$

Acceleration due to gravity $\left(\text{g}\right)=9.8\mathrm{m}/{\mathrm{s}}^2$

Step 2: Find the velocity $\left(\mathrm{v}\right)$.

$\begin{array}{rcl}\mathrm{v}& =& \sqrt{2gh}\\ & =& \sqrt{2\times 9.8\times 8}\\ & =& 12.52\mathrm{m}/\mathrm{s}\end{array}$

Step 3: Calculate the load(force),

$\mathrm{force}=\mathrm{m}\mathrm{x}\mathrm{g}$

Substitute the given value in the above formula.

$\begin{array}{rcl}\mathrm{force}& =& 100\mathrm{x}9.8\\ & =& 980\mathrm{N}\end{array}$

Step 4: Calculate the power input.

$\begin{array}{rcl}\mathrm{Power}\mathrm{input}& =& \mathrm{force}\mathrm{x}\mathrm{velocity}\end{array}$

Substitute the given value in the above formula.

$\begin{array}{rcl}\mathrm{Power}\mathrm{input}& =& 980\mathrm{x}12.52\\ & =& 12,269.6\mathrm{W}\end{array}$

Step 5: Calculate the power output.

$\begin{array}{rcl}\mathrm{Power}\mathrm{output}& =& \mathrm{Efficiency}\times \mathrm{power}\mathrm{input}\\ & =& 0.75\mathrm{x}12,269.6\\ & =& 9,202.2\mathrm{W}\end{array}$

Therefore, the correct option is (C).