1. The problem statement, all variables and given/known data A dustpan slides down a plane inclined at angle θ. Dust is uniformly dis- tributed on the plane, and the dustpan collects the dust in its path. After a long time, what is the acceleration of the dustpan? Assume there is no friction between the dustpan and plane. p=linear mass density of dust x is chosen as distance along the plane 2. Relevant equations d(mv)/dt=mgsin(θ) (net force parallel to the plane) m(x)=px 3. The attempt at a solution My solution: d(mv)/dt=mdv/dt+vdm/dt=mgsin(θ) dm/dt=pdx/dt=pv dv/dt=x'' direct substitution: px*x''+p(x')^2=pxgsin(θ) xx''+(x')^2-xgsin(θ)=0 Dimensional analysis: x(g, t, θ) must be of the form: x=Agt^2 x'=2Agt x''=2Ag Substitute into DiffEq: 2A^2g^2t^2+4A^2g^2t^2-Ag^2t^2sin(θ)=0 cancel g^2t^2 6A^2-Asin(θ)=0 A=sin(θ)/6 x''=gsin(θ)/3 My question is, is this reasoning correct?