A small block B fits inside a lot cut in arm OA which rotates in a vertical plane at a constant rate. The block remains in contact with the end of the slot closest to A and its speed is 1.4 m/s for 0 ≤ θ ≤ 150 °. Knowing that the block begins to slide when θ = 150°, determine the coefficient of

Question

A small block B fits inside a lot cut in arm OA which rotates in a vertical plane at a constant rate. The block remains in contact with the end of the slot closest to A and its speed is 1.4 m/s for [latex]0\le heta \le 15{ 0 }^{ \circ }[/latex]. Knowing that the block begins to slide when [latex] heta =15{ 0 }^{ \circ }[/latex], determine the coefficient of static friction between the block and the slot.

Accepted Answer

Draw the free body diagrams of the block B when the arm is at [latex] heta=150^{\circ}[/latex].

[latex]\begin{gathered}\dot{ u}=a_{t}=0, \quad g=9.81 \mathrm{~m} / \mathrm{s}^{2} \+ warrow \Sigma F_{t}=m a_{t}:-m g \sin 30^{\circ}+N=0 \N=m g \sin 30^{\circ} \+\swarrow \Sigma F_{n}=m a_{n}: m g \cos 30^{\circ}-F=m \frac{ u^{2}}{ ho} \F=m g \cos 30^{\circ}-\frac{m ν^{2}}{ ho}\end{gathered}[/latex]

Form the ratio [latex]\frac{F}{N}[/latex], and set it equal to [latex]\mu_{s}[/latex] for impending slip.

[latex]\mu_{s}=\frac{F}{N}=\frac{g \cos 30^{\circ}- u^{2} / ho}{g \sin 30^{\circ}}=\frac{9.81 \cos 30^{\circ}-(1.4)^{2} / 0.3}{9.81 \sin 30^{\circ}}[/latex]

[latex]\mu_{s}=0.400\blacktriangleleft[/latex]

Question 12.61: A small block B fits inside a lot cut in arm OA which rotate...

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