Rigid Body Momentum - Calculate Velocity

[fball558]

Rigid Body Momentum?

Homework Statement

**** PICTURED IS ATTACHED ***

The center of the homogeneous disk of mass m shown below has an initial velocity of v0
up the slope. Find the velocity of the disk after an elapsed time of !t, assuming that the
disk rolls without slip.

Use the following: m = 6 kg, r = 0.4 m, theta = 36.87°, Vo
= 32 m / sec and delta(t) = 8 secs .

Homework Equations

G1+ integral(F)dt = G2 where G1 = mVo and G2= mVf

The Attempt at a Solution

i drew up 2 free body diagrams. mg is acting down. A normal force acting on the contact surface at an angle of the incline plane. then friction. Friction is the only difference. initially friction will be acting down the slope because the ball is moving up the slope. but then i assumed that the 8 seconds we analyze this the ball will stop at some point and start to roll
down (due to gravity and friction) so the friction flips to go up the incline plane.

i assumed we would have to break this problem into two parts (as mentioned above) to solve it, but i am having trouble finding my time it takes for the disk to stop AND the friction force (we are not given a kinetic or static coefficient of friction)

if someone could please help me out that would be great!
thanks in advance :)

 

[espen180]

Full roll means infinite friction coefficient for all practical purposes.

HINT: Draw all acting forces in your free-body diagram. What is the torque on the disc?

 

[fball558]

what is full roll??
is that the same thing as "rolls without slip"?
i know rolls without slip means that the contact point (where the disk meets the ramp) is the Instantaneous center which means it has no velocity at that point.

 

[espen180]

Yes, that is correct.

 

[fball558]

ok that's what i though.
but how would i find how long it takes for the disk to stop. it is initially moving up the ramp. i need to find if in the 8 seconds we are looking at this, if the disk stops and goes back down. or if after the 8 seconds it is still moving up the ramp.
i tried to do the sum of the forces in the x = max (Newtons second law)
but i don't know friction force or ax.
if they just gave me the coefficient this problem would be easy :(

 

[espen180]

You may assume that the friction force at all times balances the sum of gravity and the normal force.

I'll gie you a hint: What is the kinetic energy of the disc when its center of mass has a velocity v?