Dynamics; I don't get, nor see the wrong assumption.

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Homework Help Overview

The discussion revolves around a dynamics problem involving a collar sliding along a shaft, with specific scenarios regarding the motion of the collar and the shaft. The original poster seeks clarification on the acceleration of the collar when subjected to different conditions, particularly focusing on the case where the collar experiences a downward acceleration.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to understand why their method for calculating the acceleration does not yield the expected results, particularly questioning the assumptions made about the components of acceleration. Other participants suggest that the expression for the acceleration component along the shaft may be incorrect and discuss the implications of the collar's motion relative to the shaft.

Discussion Status

Participants are actively engaging with the problem, offering insights into the components of acceleration and questioning the original poster's assumptions. There is a recognition of potential errors in the calculations, particularly regarding the y component of acceleration, but no consensus has been reached on the correct approach.

Contextual Notes

Participants note that the collar's motion is influenced by gravitational forces and the frame of reference used for measuring acceleration. There is an emphasis on the distinction between the collar's acceleration in different reference frames, which remains a point of discussion.

Pascal1p
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Homework Statement


The 2-kg collar C is free to slide along the smooth shaft AB. Determine the acceleration of collar C if (a) the shaft is fixed from moving. (b) Collar A, which is fixed to shaft AB, moves downward at constant velocity along the vertical rod, and (c) collar A is subjected to a downward acceleration of 2 m/s^2. In all cases, the collar moves in the plane.
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My question is about the case c.

Homework Equations


∑F=m*a


T3. The Attempt at a Solution
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The answer model also says that a(along shaft) does not change, so why doesn't this method work?
 
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You do not have the correct expression for the component of acceleration of the collar that is parallel to the shaft. Your expression would be correct if the collar was stuck to the shaft so that it could not slide along the shaft.

EDIT: Actually, now that I look at it again, I think this part is correct. You correctly found the component of acceleration of the collar that is along 45 degrees below the horizontal. There will also be a component perpendicular to this.

I believe your error is when you tried to find the acceleration component in y direction.
 
Last edited:
TSny said:
View attachment 103081

You do not have the correct expression for the component of acceleration of the collar that is parallel to the shaft. Your expression would be correct if the collar was stuck to the shaft so that it could not slide along the shaft.

But even the solution model says that the value of this m*a equals 2*9.81*sin(45). They use: m*a(along shaft)= 2*9.81*sin45 = 2(2cos45 + a[c relative to ab]).
Even if it not stuck to the shaft, the only force that can make it slide along shaft is the gravitational force, which won't change direction nor magnitude during the motion. The normall force is perpendicular to the motion down the shaft, so it is this 2*9.81*sin45 that is making it accelerate down the shaft.
 
Yes, I was wrong. See the edit to my first post. I don't think you got the y component of acceleration correct.
 
It's important to keep in mind that the acceleration of 6.94 m/s2 "along the shaft" that you obtained is the component of acceleration at 45 degrees below the horizontal as measured in the Earth frame of reference. It is not the acceleration of the collar relative to the shaft frame of reference.
 
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