(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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.

2. Relevant equations

F=ma

3. 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]

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# Mass on a wedge. Relative acceleration.

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