A force P of magnitude 3 N is applied to a tape wrapped around a thin hoop of mass 2.4 kg. Knowing that the body rests on a frictionless horizontal surface, determine the acceleration of (a) Point A, (b) Point B.

Question

Accepted Answer

Hoop:[latex]\overline { I } =m{ r }^{ 2 }[/latex]

[latex]\ \underrightarrow { + } \sum { { F }_{ x } } =\sum { { \left( { F }_{ x } \right) }_{ eff } } :P=m\overline { a }[/latex]

[latex]\ \overline { a } =\frac { P }{ m } \rightarrow [/latex]

[latex]\ +\curvearrowright \sum { { M }_{ G } } =\sum { { \left( { M }_{ G } \right) }_{ eff } } :Pr=\overline { I } \alpha =m{ r }^{ 2 }\alpha [/latex]

[latex]\alpha \frac { P }{ mr } \curvearrowleft[/latex]

(a) Acceleration of Point [latex]\underrightarrow { + } { a }_{ A }=\overline { a } +r\alpha =\frac { P }{ m } +r\left( \frac { P }{ mr } \right) =2\frac { P }{ m } [/latex]

[latex]\ { a }_{ A }=2\frac { 3N }{ 2.4kg } =2.5m/{ s }^{ 2 }[/latex]

[latex]\ { a }_{ A }=2.50m/{ s }^{ 2 }[/latex]

(b) Acceleration of Point B. [latex]\underrightarrow { + } { a }_{ A }=\overline { a } -r\alpha =\frac { P }{ m } +r\left( \frac { P }{ mr } \right) =0\ \[/latex]

[latex]{ a }_{ B }=0[/latex]

Question : A force P of magnitude 3 N is applied to a tape w...