Canisters Rolling Down a Half Pipe

[onegreatweb]

Homework Statement

Oddjob rolls a canister of nerve gas twoards Bond, who is at the bottom of a curved trench. The canister has a mass of 16 kg, a radius of r = 0.8 m, and a rotational inertia of 10 kg*m2. It starts with no velocity. If the trench has a radius of R = 3.5 m, how fast is the canister moving when it reaches Bond?

Homework Equations

Conservation of Energy: E_i = E_f

The Attempt at a Solution

PE_i = KE_f + KE_rotation
mgR = (1/2)m*v_f² + (1/2)I*ω²
mgR = (1/2)m*v_f² + (1/2)I*(v_f/R)²
mgR = v_f² (m/2 +I/(2R²))
v_f² = (2*m*g*R³) / (m*R² + I)
v_f = sqrt((2*m*g*R³) / (m*R² + I))

I plugged in all the numbers but the computer says this is incorrect. Where did I go wrong?

Edit: I posted the wrong question initally. Oops. This is the correct one with the correct image.

 

[Doc Al]

Is Bond at the bottom of the trench? Or on the opposite side?