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## Homework Statement

A right triangular prism ABD with inclination angle 30degrees and mass m can slide without friction along smooth horizontal surface. A uniform solid cylinder of mass m rolls down the inclined surface AB without friction. If both cylinder and prism are at rest initially, what will be the relative velocity and absolute velocity of the cylinder’s center O after its height decreased by h?

Hints: 1. You may use conservation of momentum principle for the system cylinder-prism to relate velocities of prism and of cylinder’s center (absolute and relative )

2. When you apply conservation of energy relation do NOT forget to account for kinetic energy of the cylinder’s rotation.

## Homework Equations

Pe=mgh

KE = 1/2Iω^2 and 1/2mv^2

m1v1=m2v2

Vabs = Vrel-Vprism

## The Attempt at a Solution

2gh=V^2 +V^2+Vprism^2

MsystemVprism=MSystem(Vrel(i)-Vprism)

Vprim=((Vrel√3)/4) - My professor said this was correct.

So, this is where I get stuck because I am not sure which V to use for the rotational energy or the translational energy. I tried using Vrel for everything and I get the wrong answer. I think I am suppose to use Vabsolute for the velocities of the cylinder, but that gives me some ugly math which I think is wrong.

Any help would be helpful, and I really appreciate it!