Question

A fan motor uses 8310 J of energy in 9.44 s. This energy is used to accelerate a 8.12 kg blade to 19.7m/s in 3.10 s. What is the efficiency of the fan? Leave your answer as a decimal.

Answer 1

Solution.

$W_m=8310J;$

$t_m=9.44s;$

$m=8.12kg;$

$v=19.7m/s;$

$t=3.10s;$

$W_K=\dfrac{mv^2}{2};$

$W_K=\dfrac{8.12\sdot19.7^2}{2}=1575.6J;$

$P_{out}=\dfrac{W_K}{t};$

$P_{out}=\dfrac{1575.6}{3.10}=508.3w;$

$P_{in}=\dfrac{8310}{9.44}=880.3w;$

$efficiency=\dfrac{P_{out}}{P_{in}};$

$efficiency=\dfrac{508.3}{880.3}=0.58;$

Answer:$efficiency=0.58;$