Distance the hoop travels up the incline

[vbrasic]

Homework Statement

A ring (hollow cylinder) of mass 2.61kg, inner radius 6.35cm, and outer radius 7.35cm rolls (without slipping) up an inclined plane that makes an angle of θ=36.0°, as shown in the figure below. At the moment the ring is at position x = 2.19m up the plane, its speed is 2.61m/s. The ring continues up the plane for some additional distance and then rolls back down. It does not roll off the top end. How much further up the plane does it go?

Homework Equations

$T=RF=I\alpha$
$\omega_f^2=\omega_i^2+2\alpha d$

The Attempt at a Solution

My proposed way to solve the problem is this:

I calculated the gravitational force down the ramp. This force is 15.034 N. It exerts a torque on the hoop of $15.034N\times 0.0735 m$. Torque is also equal to $I\alpha$. I can calculate $I$. Dividing by it will give me angular acceleration. Then I can solve for the angular distance it takes for the hoop to stop rolling up the hill. Does this approach make sense?

 

[phinds]

Homework Statement

A ring (hollow cylinder) of mass 2.61kg, inner radius 6.35cm, and outer radius 7.35cm rolls (without slipping) up an inclined plane that makes an angle of θ=36.0°, as shown in the figure below. At the moment the ring is at position x = 2.19m up the plane, its speed is 2.61m/s. The ring continues up the plane for some additional distance and then rolls back down. It does not roll off the top end. How much further up the plane does it go?

Homework Equations

$T=RF=I\alpha$
$\omega_f^2=\omega_i^2+2\alpha d$

The Attempt at a Solution

My proposed way to solve the problem is this:

I calculated the gravitational force down the ramp. This force is 15.034 N. It exerts a torque on the hoop of $15.034N\times 0.0735 m$. Torque is also equal to $I\alpha$. I can calculate $I$. Dividing by it will give me angular acceleration. Then I can solve for the angular distance it takes for the hoop to stop rolling up the hill. Does this approach make sense?

Just FYI, there IS no "figure below"

 

[kuruman]

Does this approach make sense?

Can you provide expressions instead of numbers? That way it would be easier to check your work.

 

[Orodruin]

While you can do it by using a force and torque analysis, there are many things that you need to be careful with, things that we cannot tell whether you got them right or not unless you provide your working. Also, it is (quite a lot) simpler to use energy arguments.