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A body is placed on a rough inclined plane whose coefficient of friction is μ. Let F₁ be the least force needed to just move the body upward along the plane, and F₂ be the least force needed to just keep it from slipping downward. If the plane is inclined at an angle θ to the horizontal and tan θ = 2μ, then what is the value of F₁/F₂?

1. 1
2. 2
3. 3
4. 4

Correct answer: 3

Solution

The ratio F₁/F₂ can be derived from the forces acting on the body on the inclined plane. Since F₁ must overcome both the gravitational component pulling the body down and the friction opposing the upward movement, while F₂ must counteract the gravitational pull and the friction acting downwards, the relationship simplifies to F₁ being three times F₂ when tan θ = 2μ.

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