- #1

derravaragh

- 24

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## Homework Statement

A skier slides down a giant snowball (= sphere of radius R) with negligible friction. H starts at the top with very small velocity. Determine the angle θ_f where the skier will come off the surface. Use these principles of dynamics: (1) Energy is a constant of the motion. (2) The normal force of the contact decreases as the skier descends, and N = 0 at the point where the skier comes off the surface. (3) a = R*alpha*t(hat) - R*(w^2)*r(hat) where a is the acceleration vector, t(hat) is the time vector, and r(hat) is the position vector.

## Homework Equations

E = KE + U where E is energy, KE is kinetic energy, and U is potential energy (I understand these may not be the standard)

KE = (1/2)mv^2

## The Attempt at a Solution

For this problem, I am at a loss for what to do. I've worked it out a few times, taking into account all the factors. Using the first principle, I determined the initial kinetic energy is 0 as the initial velocity is so small, it's negligible, and the initial potential energy is merely 2Rmg. Next, I determined the final kinetic energy to be (1/2)mv^2 and final potential to be mg(R+Rcosθ_f).

Therefore, the energy equation is: 2Rmg = (1/2)mv^2 + mg(R+Rcosθ_f)

Next, I considered the fact that the centripetal force = the normal force, therefore at the point when the skier leaves the surface, the acceleration is only reliant on the tangential acceleration.

This is where I get confused. I can't seem to figure out how to make the connection between the acceleration and velocity for this problem, and be able to solve for θ_f.

Where should I go from here, assuming I'm even on the right track.