1. two identical bowling balls of mass m and radius r roll side by side at speed v0 along a flat surface. ball 1 encounters a ramp of angle θ that has a tacky surface and rolls up without slipping until it reaches a maximum height h1. ball 2 encounters a ramp of angle θ that has a frictionless surface which it ascends to a maximum height h2. what is the ratio of h1/h2 in terms of m, v0, θ, g, and r?

1/2

Explanation:

We need to make a couple of considerations but basically the problem is solved through the conservation of energy.  

I attached a diagram for the two surfaces and begin to make the necessary considerations.

Rough Surface,

We know that force is equal to,

Matching the two equation we have,

Applying energy conservation,

Frictionless surface

Given the description we apply energy conservation taking into account the inertia of a sphere. Then the relation between and is given by

electrical to thermal

it about 600 mph from what i calculated