Answer to Question #169369 in Mechanics | Relativity for buddy

Question

A fan motor uses 6630 J of energy in 8.80 s. This energy is used to accelerate a 12.9 kg blade to 26.5 m

s

ms in 7.75 s. What is the efficiency of the fan? Leave your answer as a decimal.

Answer 1

work done in accelerating the fan is equal to change in it's $K.E=1/2\times 12.9\times26.5^2$

$W=4529.5125J$

rate of work done $=W/t=4529.5125/7.75=584.45w$

rate of work done by motor$=P_{in }= 6630/8.8=753.41w$

$efficiency= \frac{P_{out}}{P_{in}}\times100 \%=\frac{584.45}{753.41}\times 100\%=77.6\%$