Answer to Question #176112 in Mechanics | Relativity for Akinola Agboola

Question

A load of mass 150kg is to be pulled up a smooth plane at 15 degrees to the vertical. Calculate the minimum force required to pull it up the plane if the plane is 75%efficient

Answer 1

Solution.

$m=150kg;$

$\alpha=15^o;$

$\eta=75$ %;

$F-?;$

$\eta=\dfrac{A}{A_f}\sdot100$ % $\implies A=\dfrac{\eta A_f}{100\%};$

$A=mgh;$

$A_f=Fl;$

$sin(90-\alpha)=\dfrac{h}{l} \implies h=lsin(90-\alpha);$

$mglsin(90-\alpha)=\dfrac{\eta Fl}{100\%};$

$mgsin(90-\alpha)=\dfrac{\eta F}{100\%}\implies F=\dfrac{mgsin(90-\alpha)\sdot100\%}{\eta};$

$F=\dfrac{150kg\sdot9.8ms^{-2}\sdot 0.966\sdot100\%}{75\%}=1893.36N;$

Answer:$F=1893.36N.$