The support bracket shown is used to transport a cylindrical can from one elevation to another. Knowing that μs = 0.25 between the can and the bracket, determine (a) the magnitude of the upward acceleration a for which the can will slide on the bracket, (b) the smallest ratio h/d for which the can

Question

The support bracket shown is used to transport a cylindrical can from one elevation to another. Knowing that [latex]{ \mu }_{ s }=0.25[/latex] between the can and the bracket, determine (a) the magnitude of the upward acceleration a for which the can will slide on the bracket, (b) the smallest ratio h/d for which the can will tip before it slides.

Accepted Answer

(a) Sliding impends

[latex]\overset{+}{\longrightarrow } {{\Sigma F_{y}=\Sigma(F_{x})_{\mathrm{eff}}\,\!:~~~}}{{~~~F=m a\cos30^{\circ}}}[/latex]

[latex]+\uparrow\,\Sigma F_{y}=\Sigma(F_{y})_{\mathrm{eff}}\,;\quad N-m g=m a\,\mathrm{sin}\,30^{o}[/latex]

[latex]N=m(\,g+a\sin30^{\circ})[/latex]

[latex]\mu_{s}={\frac{F}{N}}[/latex]

[latex]0.25=\frac{m a\cos30^{\circ}}{m(g+a\sin30^{\circ})}[/latex]

[latex]g+a\sin30^{\circ}=4a\cos30^{\circ}[/latex]

[latex]{\frac{a}{g}}={\frac{1}{4\cos30^{\circ}-\sin30^{\circ}}}[/latex]

[latex]\mathbf{a}=0.337\,g\ ⦨30^{\circ}\blacktriangleleft[/latex]

(b) Tipping impends

[latex]\circlearrowleft \Sigma M_{G}=\Sigma(M_{G})_{\mathrm{eff}}\colon~~F\biggl\lgroup{\frac{h}{2}}\biggr\rgroup-N\biggl\lgroup{\frac{d}{2}}\biggr\rgroup=0[/latex]

[latex]{\frac{F}{N}}={\frac{d}{h}}[/latex]

[latex]\mu=\frac{F}{N};\quad0.25=\frac{d}{h};[/latex]

[latex]{\frac{h}{d}}=4.00\blacktriangleleft[/latex]

Question 16.7: The support bracket shown is used to transport a cylindrical...

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