A 20-kg cabinet is mounted on casters that allow it to move freely (μ = 0) on the floor. If a 100-N force is applied as shown, determine (a) the acceleration of the cabinet, (b) the range of values of h for which the cabinet will not tip.

Question

A 20-kg cabinet is mounted on casters that allow it to move freely [latex](\mu=0)[/latex] on the floor. If a 100-N force is applied as shown, determine (a) the acceleration of the cabinet, (b) the range of values of h for which the cabinet will not tip.

Accepted Answer

(a) Acceleration

[latex]\begin{aligned}& \overset{+}{\longrightarrow } \Sigma F_{x}=\Sigma(F_{x})_{\mathrm{eff}}\,\colon\ \ 100\ \mathrm{N}=m\bar{a}\& \quad\quad\quad\quad 100\,\mathrm{N}=(20\,\mathrm{kg})\overline{{{a}}}\& \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \overline{{{\mathbf{a}}}}=5.00\;\mathrm{m/s}^{2}\longrightarrow\blacktriangleleft\end{aligned}[/latex]

(b) For tipping to impend [latex]\circlearrowright :\quad\quad A=0[/latex]

[latex]\begin{aligned}& +\circlearrowright \Sigma M_B=\Sigma(M_{B})_{\mathrm{eff}}:\quad(100\ \mathrm{N})h-m g(0.3\ \mathrm{m})=m\bar{a}(0.9\ \mathrm{m})\& \quad\quad (100\ \mathrm{N})h-(20\mathrm{~kg})(9.81\ \mathrm{m/s^{2}})(0.3\ \mathrm{m})=(100\ \mathrm{N})(0.9\ \mathrm{m})\& \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad h=1.489\,\,{\mathrm{m}}\end{aligned}[/latex]

For tipping to impend [latex]\circlearrowleft : \quad\quad B=0[/latex]

[latex]\begin{aligned}& +\circlearrowright \Sigma M_A=\Sigma(M_A)_{eff}:\quad(100\ N)h+m g(0.3\mathrm{\ m})=m\bar{a}(0.9\mathrm{\ m})\& \quad\quad (100\ \mathrm{N})h+(20\ \mathrm{kg})(9.81\ \mathrm{m/s}^{2})(0.3\ \mathrm{m})=(100\ \mathrm{N})(0.9\ \mathrm{m})\& \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad h=0.311\ \mathrm{m}\end{aligned}[/latex]

Cabinet will not tip: [latex]\quad\quad\quad\quad 0.311\,\mathrm{m}\leq h\leq1.489\,\mathrm{m}\blacktriangleleft[/latex]

Question 16.9: A 20-kg cabinet is mounted on casters that allow it to move ...

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