question_answer

A plank, 8 m long, has one end 1 m higher than the other. What minimum force parallel to the plank will be necessary to push a box up it, the box and its contents having a mass of 100 kg and the coefficient of sliding friction between it and the plank being 0.3 ?

A)  50.2 kgf         

B)         25.5 kgf

C)  75.0 kgf         

D)         42.3 kgf  

Correct Answer: D

Solution :

            \[F=mg\sin \theta +\mu mg\cos \theta \] In the diagram,             \[\sin \theta =\frac{1}{8}\]and\[\cos \theta =\frac{\sqrt{63}}{8}\cong 1\] \[\therefore \]      \[F=100\left( \frac{1}{8}+0.3 \right)g\]             \[=100(0.125+0.3)kg\,\,f\]