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## Homework Statement

A ball of mass m is given an initial velocity ⃗v and entered into a funnel. Model the acceleration of the ball over a period of time.

Note: I don't have a full problem statement because this isn't really a homework question (but I figured it was homework-like enough to post here instead of the general physics subforum). Is this the wrong place to post it?

## Homework Equations

Fg = mg

Fnet=Σ ⃗F=m ⃗a

Centripetal acceleration = v

^{2}/r

## The Attempt at a Solution

If the initial velocity is too high, I know the inertia of the ball will cause it to expand its orbital radius... the ball will move away from the center of the funnel (up and outwards) until equilibrium is achieved.

At equilibrium, I know that:

1. The vertical component of the normal force (Fn) will balance the force of gravity (net vertical force = 0).

2. The horizontal component of Fn will be the force required to achieve stable centripetal acceleration at the current velocity and radius (m*(v^2)/r).

But how can I calculate how fast the ball accelerates away from the center of the funnel in this situation (when initial velocity is higher than equilibrium conditions)? Is the normal force constant?

Also what about how kinetic energy is increased by traveling into (down) the funnel?

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