Homework H3.B - Sp23

 Problem statement Solution video

DISCUSSION

It is recommended that you use the moving reference frame kinematics equations relating the motions of A and B:

vA = vB + (vA/B)rel + ω x rA/B
aA = aB + (aA/B)rel + α x rA/B + 2ω x (vA/B)rel + ω x (ω x rA/B)

Attaching the observer and the xyz-axes to bar ACD prescribes ω and α  to be the angular velocity and angular acceleration, respectively, of ACD. What do you use for the relative velocity and relative acceleration terms, (vA/B)rel  and (aA/B)rel ? Note that although B is a fixed point (zero velocity and zero acceleration), the observer on ACD sees B moving along the slot. The magnitudes of these relative velocity and acceleration terms are unknowns, however, the two vectors are aligned with the slot; that is, they have only y-components.

12 thoughts on “Homework H3.B - Sp23”

1. William Grant Dierking says:

I keep getting a (Vb/a)rel that is in the negative j when I do my calculations, but B appears to be moving upward from the perspective of A in the animation. Am I doing my calculations wrong, or is my understanding of what (Vb/a)rel incorrect?
Thank you

1. Benjamin Carl Wassgren says:

At the start of the animation (like in the conditions given by the problem) I think that B is moving down towards the moving reference frame. It only starts to move upward when the long section of the bar is close to perpendicular with the slope.

2. Benjamin Carl Wassgren says:

How are we supposed to find (vA/B)rel)? If we use the x and y components of the equation:
vA = vB + (vA/B)rel + ω x rA/B
we are left with 3 unknowns and 2 equations (ω, (vA/B)rel in the x direction, and (vA/B)rel in the y direction).
I don't think that the stationary reference frame helps at all since ω_AB != ω.
Is there something that I am missing here?

1. CMK says:

As xyz and the observer move with the L-shaped bar, the observer always sees B moving in the y-direction; that is, the x-component of (a_B/A)_rel is zero.

1. Benjamin Carl Wassgren says:

When I fully work out the problem using (vB/A)rel only in the y direction, I end up getting:
ω in the -k direction
(vB/A)rel in the -y direction
α in the -k direction
I think the values for (vB/A)rel and α make sense, but in the animation it looks like the reference frame is rotating in the +k direction (opposite the direction I calculated for ω) so I am unsure about my answers. I am confident in my math, so I am not sure if I have set up the problem wrong or if I have misread the animation.

1. Benjamin Carl Wassgren says:

never-mind, I had reversed the signs for the vector rB/A

3. eaub says:

Would the magnitude of aB/A be 0? Considering vA is constant, wouldn't vB/A also be constant?