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Darth Frodo
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Homework Statement
A particle of mass M is on a wedge of mass 2M. The wedge is smooth, and is inclined at 30* to the horizontal. The system is released from rest. Find the acceleration of the wedge, and find the acceleration of the particle relative to the wedge.
Homework Equations
F=ma
The Attempt at a Solution
Particles motion parallel to the wedge
F=ma
(mg)sin30 = m[f - (a)cos30]
mg = 2mf - ma[itex]\sqrt{3}[/itex]Particles motion perpendicular to the wedge
F = ma
(mg)cos30 - R = m(asin30)
mg[itex]\sqrt{3}[/itex] -2R = ma
R = [itex]\frac{m(g\sqrt{3} - a)}{2}[/itex]Wedges Motion
F = ma
Rsin30 = 2ma
R = 4ma
Substitution
[itex]\frac{m(g\sqrt{3} - a)}{2}[/itex] = 4ma
mg[itex]\sqrt{3}[/itex] - ma 8ma
g[itex]\sqrt{3}[/itex] - a = 8a
g[itex]\sqrt{3}[/itex] = 9a
a =[itex]\frac{g\sqrt{3}}{9}[/itex]
The answer at the back of the book is [itex]\frac{g}{3\sqrt{3}}[/itex]