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unscientific

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## Homework Statement

a)A snowball, initially of mass m

_{0}, slides down a slope of incline angle ∅. As it moves, mass of additional snow Δm = αx. Write down the differential equation of translational motion for the snowball, ignoring rotation and friction.

b)If the snowball starts from rest, derive an expression for its velocity as a function of time.

c)A spherical ball of mass m and radius r rolls down a slope at an angle ∅. Find the frictional force required between the slope and the ball if there is no slipping.

## The Attempt at a Solution

(a)

By using conservation of momentum at t and t+Δt, where taking the limit Δt→0,

Δp/Δt = mg sin ∅

I arrive at:

(b)

I change the differential equation to dv/dm first, then use a substitution.

(c)

For part (c), do I assume that it is pure rolling?