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## Homework Statement

A snowball, initially of mass m, slides down a slope inclined at an angle φ with respect to the horizontal. As it moves, the mass of additional snow Δm = αx that it accumulates is proportional to the distance travelled x. Write the differential equation

of translational motion for the snowball, ignoring rotation and friction

## Homework Equations

Conservation of momentum [itex]mv_before =mv_after [\itex]

## The Attempt at a Solution

##dp= (m+dm)(v+dv)-mv##

##dp= mdv +vdm ##

[itex]\frac{dp}{dt}= m\frac{dv}{dt}+v\frac{dm}{dt} [/itex]

[itex]mg sin(φ) = m\frac{dv}{dt}+vαx [/itex]

But this doesn't seem right to me

Many thanks :)