Kinetic Friction and Hemispherical Dome

[engineer2b]

Homework Statement

There is a hemispherical dome that sits on a horizontal plane. It has a radius of 10m.
A 2 kg block sits on top of the dome.

Pt. 1: Assuming the coefficient of kinetic friction is 0, at what angle, θ, will it leave the dome?

Pt. 2: Assuming that μk is 0.3, what is the minimum initial velocity for which the block will leave the dome, and what angle will it leave?

Homework Equations

The Attempt at a Solution

When the block leaves the surface, there will cease to be any kinetic friction. It would seem as though the block would have to leave the dome at, or before pi/4; however, I could be incorrect in that inference.

 

[nrqed]

Homework Statement

There is a hemispherical dome that sits on a horizontal plane. It has a radius of 10m.
A 2 kg block sits on top of the dome.

Pt. 1: Assuming the coefficient of kinetic friction is 0, at what angle, θ, will it leave the dome?

Pt. 2: Assuming that μk is 0.3, what is the minimum initial velocity for which the block will leave the dome, and what angle will it leave?

Homework Equations

The Attempt at a Solution

You must show what you have tried so far. Hint: what is special about the forces at the instant when the block leaves the surface?