Question

What happens to kinetic energy of a snowball as it rolls across the lawn and gains mass

Answer 1

The momentum, p(t)=m(t)⋅v(t), of the snowball should remain constant as there is no external force acting on the system, that is the snowball and the snowflakes it gathers, in the direction of travel.

i.e. ΣF=.p=0 so p=const.

As for KE, T(t)=12mv2=p22m=const.m

as mass is increasing, KE should decrease

this has greatly simplified it all, as it looks at it as a point mass

Answer 2

it will decreases