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

Question #176112

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


1
Expert's answer
2021-03-29T09:01:20-0400

Solution.

m=150kg;m=150kg;

α=15o;\alpha=15^o;

η=75\eta=75%; %;

F?;F-?;

η=AAf100\eta=\dfrac{A}{A_f}\sdot100 %     A=ηAf100%;\implies A=\dfrac{\eta A_f}{100\%};

A=mgh;A=mgh;

Af=Fl;A_f=Fl;

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

mglsin(90α)=ηFl100%;mglsin(90-\alpha)=\dfrac{\eta Fl}{100\%};

mgsin(90α)=ηF100%    F=mgsin(90α)100%η;mgsin(90-\alpha)=\dfrac{\eta F}{100\%}\implies F=\dfrac{mgsin(90-\alpha)\sdot100\%}{\eta};

F=150kg9.8ms20.966100%75%=1893.36N;F=\dfrac{150kg\sdot9.8ms^{-2}\sdot 0.966\sdot100\%}{75\%}=1893.36N;


Answer:F=1893.36N.F=1893.36N.




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