First slide

Rotational motion

Question

Equilibrium of two Planks on a Rough Plane: Figure shows two planks inclined to horizontal rough surface and connected by a string. Find the minimum angle $θ$ (in degrees) for which this system remain in equilibrium if friction coefficient is $μ$ = 0.5.

Moderate

Solution

For equilibrium of plank, we use
$\begin{array}{l} N = mg \\ T = μN = μmg . \end{array}$
For rotational equilibrium of plank we use torque on plank about any point must be zero.
$τ_{A} = mg \times l / 2 \cos θ - T \times lsin θ = 0$
$\frac{mgl}{2} \cos θ = μmgl sinθ$
$tanθ = \frac{1}{2 μ} = 1 \Rightarrow θ = 45^{\circ}$

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