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
Solution.
m=150kg;m=150kg;m=150kg;
α=15o;\alpha=15^o;α=15o;
η=75\eta=75%;η=75 %;
F−?;F-?;F−?;
η=AAf⋅100\eta=\dfrac{A}{A_f}\sdot100η=AfA⋅100 % ⟹ A=ηAf100%;\implies A=\dfrac{\eta A_f}{100\%};⟹A=100%ηAf;
A=mgh;A=mgh;A=mgh;
Af=Fl;A_f=Fl;Af=Fl;
sin(90−α)=hl ⟹ h=lsin(90−α);sin(90-\alpha)=\dfrac{h}{l} \implies h=lsin(90-\alpha);sin(90−α)=lh⟹h=lsin(90−α);
mglsin(90−α)=ηFl100%;mglsin(90-\alpha)=\dfrac{\eta Fl}{100\%};mglsin(90−α)=100%ηFl;
mgsin(90−α)=ηF100% ⟹ F=mgsin(90−α)⋅100%η;mgsin(90-\alpha)=\dfrac{\eta F}{100\%}\implies F=\dfrac{mgsin(90-\alpha)\sdot100\%}{\eta};mgsin(90−α)=100%ηF⟹F=ηmgsin(90−α)⋅100%;
F=150kg⋅9.8ms−2⋅0.966⋅100%75%=1893.36N;F=\dfrac{150kg\sdot9.8ms^{-2}\sdot 0.966\sdot100\%}{75\%}=1893.36N;F=75%150kg⋅9.8ms−2⋅0.966⋅100%=1893.36N;
Answer:F=1893.36N.F=1893.36N.F=1893.36N.
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