The minimum force required to start pushing a body up a rough (having co-efficient of friction μ ) inclined plane is F 1 while the minimum force needed to prevent it from sliding is F 2 . If the i

Question

The minimum force required to start pushing a body up a rough (having co-efficient of friction μ ) inclined plane is F 1 ​ while the minimum force needed to prevent it from sliding is F 2 ​ . If the inclined plane makes an angle θ with the horizontal such that tan θ = 2 μ , then the ratio F 1 ​ / F 2 ​ is

TestHub · Accepted Answer

When body is being prevented from sliding down $F_{m i n} = F_{2} = m g sin θ - μ m g cos θ F_{2} = m g sin θ - μ m g cos θ$ When body is pushed up friction acts downward $F_{1} = mg sin θ + μ mg cos θ$ $F_{1} - F_{2} = 2 μ mg cos θ F_{1} + F_{2} = 2 m g sin θ} \frac{F _{1} + F _{2}}{F _{1} - F _{2}} = \frac{t a n θ}{μ} = 2 : 1 \Rightarrow \frac{2 F _{1}}{2 F _{2}} = \frac{2 + 1}{2 - 1}$ or, $\frac{F _{1}}{F _{2}} = 3 : 1$

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