Apr 1, 2008
Problem No. 6/129
For this problem, when the kinetic energy expression is written are both KE terms included (i.e. translational and rotational)? I did it with both but got a different answer. When only including the translational component I get the right answer but it doesn't make sense to me since the door is rotating also. Any insight?
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7 comments:
Good question, I don't know the answer, but what you're saying makes sense. Maybe the rotational KE is considered to be negligible? Doesn't seem likely to me, considering it's a 200-pound garage door.
MY question is this: Given the way the spring/pulley assembly is set up, wouldn't the spring deflection be half of the distance that point A travels?
I got the 'correct' answer by neglecting the rotational component of KE and assuming that BOTH springs deflect 8 feet each.
It just doesn't seem to me that this should be correct. The pulley that is attached to the end of each spring should halve the deflection with respect to the change in position of point A... Right?
Also, just had a thought...
There is no rotational KE because in the final position, the door is no longer rotating: at that point it is straight up and down in it's tracks. I don't know if that's right or not, but I would bet it's the reason.
I agree with NCK's explanation that the door has no rotational KE at position 2 -- at that position the door is in pure translation.
I just checked the solution; it shows a 4 foot stretch in EACH spring. This agrees with NCK's explanation but does not for some reason agree with the results that NCK is reporting. Check over your work to make sure that there are no numerical errors. Let me know if you are not able to find the problem.
I was using the force required to stretch the springs 8-feet each, not the potential energy resulting from maintaining a 4-foot stretch in each.
(2)(50 lb/ft)(8 ft) = 800 lb
(2)(0.5)(50 lb/ft)(4 ft)^2 = 800 lb-ft
Equal numerical values, immensely different units. This explains the "correct" answer, although it was arrived at by a wholly incorrect method.
In my error, the only way to get a correct potential spring "energy" was to use an 8-foot deflection. Units, units, units...and the correct equations never hurt, either!
Oh yea, there are TWO springs... guess that could explain why my answer is off by a factor of 2. Hooray details..
Could please someone explain why the springs stretch 4 feet? I would think they would stretch only 2 feet because they are connected to 2 ropes while the door is only connected to 1,
so,
L_rope = x + 2*y + constants
or does that technique not apply here?
For NCK:
Thanks for explaining the fact that at the end when the door shuts there is no translation. I neglected to see that there was no rotation at the final position.
For Mark:
A simple static analysis will show why the strings stretch 4 ft each. First do and FBD with the door and the cables... the door weighs 200 lb. and there are 2 cables, thus the tension on each is 100 lb.
Second and last make an FBD of one of the pulleys.... two cable tension forces of 100 lb and one spring force. You will find that Fsp = 200lb, divide that by the k =50lb/ft and you will find a deflection of 4ft.
Remember to use 2 springs in your WE analysis otherwise you wont get the right answer.
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