Question Number 52043 by ajfour last updated on 02/Jan/19
Commented by ajfour last updated on 02/Jan/19
$${Except}\:{ground}\:{all}\:{suraces}\:{are} \\ $$$${frictionless}.\:{An}\:{wedge}\:{has}\:{to} \\ $$$${support}\:{two}\:{cyliners}\:{one}\:{top}\:{of} \\ $$$${another}\:{against}\:{wall}.\:{Find} \\ $$$${minimum}\:\mu\:{on}\:{ground}\:{for} \\ $$$${needed}\:{equilibrium}. \\ $$
Answered by mr W last updated on 02/Jan/19
$${N}={normal}\:{force}\:{between}\:{ball}\:{and}\:{wedge} \\ $$$${N}\:\mathrm{cos}\:\alpha=\left({m}+{m}_{\mathrm{0}} \right){g} \\ $$$$\Rightarrow{N}=\frac{\left({m}+{m}_{\mathrm{0}} \right){g}}{\mathrm{cos}\:\alpha} \\ $$$${N}\:\mathrm{sin}\:\alpha\leqslant\mu\left({M}+{m}+{m}_{\mathrm{0}} \right){g} \\ $$$$\Rightarrow\mu\geqslant\frac{\left({m}+{m}_{\mathrm{0}} \right)\mathrm{tan}\:\alpha}{{M}+{m}+{m}_{\mathrm{0}} } \\ $$
Commented by ajfour last updated on 02/Jan/19
$${Very}\:{nice}\:{Sir},\:{i}\:{mistook}\:{it}\:{might} \\ $$$${be}\:{little}\:{interesting}. \\ $$
Commented by mr W last updated on 02/Jan/19
$${it}\:{makes}\:{no}\:{difference}\:{if}\:{it}\:{is}\:{one}\:{ball} \\ $$$${or}\:{more}\:{balls},\:{i}\:{think}. \\ $$