I tried to solve the problem by using work-energy equation, and got
T1 = 1/2*mv_1^2 + 1/2 *Iomega_1^2
T2 = 1/2*mv_2^2 + 1/2 *Iomega_2^2
so I had v_2, omega_1, omega_2, 3 unknowns, and I only have one equation, where do I go from there?
I tried using newton-euler equations too, but didn't get enough equations to solve the problem either. Any suggestions?
5 comments:
You are on the right track. You have to use the work energy eqaution to relate between the v_2, w_1 and w_2, this is your first equation.
Now for the second equation you would use kinematics, for position -1 and position-2 to relate v-1 to w-1 and v-2 to w-2.
From position- 1, you will get:
v-1 = v-c(no-slip=0)+(w_1*r)
We are given the value for v-1, substitute to get w_1.
For the other equation:
position-2
v-2= v-c(no-slip=0)+(w_2*r)
therefore substitue all these results back into the work energy equatuion, and you will see that the only unknown that you have would be v-2.
Once you get v-2, then use Newton's equation at position-2, to find the Normal force N.
Sum(F(n-direction)) = N - mg = m*an
N - mg= ((v-2)^2)/r
Only unknown is N.
Hope you understood this,
See you.
Thank you for you explanation, makes perfect sense.
The height that the center of mass of the wheel drops is hard to find. I know that it will be the radius of the wheel off of point A (6"), but how do you find the height it drops on the incline?
It is a whole lot of trig. Call 6" above point A the datum line and the center of the circle the starting point. This is the total change in height.
Start from the point where the disk contacts the slope. Find the height difference between the that point and the center of the circle. Next find the height difference from the point where the circle touched the slope to where the plane turns into a curved path. you know the distance from the point in space to point A and also the distance from that same point to where the incline turns into the curved path. drawing a horizontal line may help. You can now find the change in height between point A and the inclined point. Add up all of the heights and do not forget to take away the radius of the circle and you should be all set.
Assume that the radius of the circle is perpendicular to the path. This gives the angle of the slope as 60 degrees from the horizontal.
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