Find the velocity of block a using vector method.

[Dusty912]

Homework Statement

(Picture attached)

Question 1: The system starts at rest. Block a accelerates towards the bottom the the rod. Find the velocity of the block when it is at the bottom of the rod using the "vector method". So this was my midterm question today. I knew how to figure out how fast it was going using work emery method and found the velocity to be 3.16 meters per second which I know is the right answer. But, I cannot find anything about a "vector method" could someone help me understand what this is indicating?

Question 2: find the tension in the string. I believe I found this to be about 264.9 by finding out how fast block A is accelerating and then applying the dynamic equilibrium force equation and solving for T

Homework Equations

L=2X_a +X_b (the length of the string that is changing with time)

F=ma (in y-direc)

for block A

2T-m_ag=m*_a

The Attempt at a Solution

question 1:
applying a time derivative to L yields
0=2x'_a+x'_b

and taking another:
0=2x''_a+x''_b
Ill stop here for question 1 because I am just wondering what vector method is indicating to do. The correct velocity is 3.16m/s (I know this is correct)

question 2:

if block a moves .6 meters from initial velocity zero to velocity 3.16 then it is accelerating at 8.32 m/s² by applying the kinematics equation. by subbing in my values to :

2T-m_ag-500=m*_a

I got T=264.9NI also applied the dynamic equilibrium expression to block B and got the same result
is this correct?
for block B T-mg=ma

acceleration of B is 16.64
subbing in the values gets 264.9 again.

This seems fairly straightforward for question 2 but a lot of people I talked to had different answers.
by the way for the first question, I know you all have a policy that you do not give solutions, but I have already taken the exam and am just wondering what I should have done instead. The second question just needs to be reviewed. Thanks ahead of time. you all rock!

 

[haruspex]

using the "vector method"

That doesn't make much sense to me either. My best guess is that they mean using forces and accelerations rather than energy.
Using that approach, I agree with your answers.

 

[Dusty912]

Yea, he also asked us to write an FBD with normal and tangential coordinate, even though the motion is linear. It was only until a student said something that he corrected himself. I'm a first year transfer and don't understand why my community college professors were so phenomenally talented at what they do, while the professors at my four year have been somewhat disappointing. I was babied and didn't even know it :(

but, great. I'm glad I got the tension right at least

 

[Dusty912]

thanks for your help! you rock!

 

[Dusty912]

Hey I've got another question for you regarding the wording of that question. In an earlier part of the problem he asked to "derive the dynamic force equilibrium equations" which I put as F=ma applied separately to block A and B, and then expanded as I earlier stated to find the tension. Should he have just said "find the velocity of block A with the dynamic equilibrium equations" instead of "vector method"? I don't understand why he would change terminology in the middle of a problem. Unless I am misunderstanding something here and the two are not related. This problem was my whole midterm by the way.

 

[Dusty912]

That doesn't make much sense to me either. My best guess is that they mean using forces and accelerations rather than energy.
Using that approach, I agree with your answers.

Hey I've got another question for you regarding the wording of that question. In an earlier part of the problem he asked to "derive the dynamic force equilibrium equations" which I put as F=ma applied separately to block A and B, and then expanded as I earlier stated to find the tension. Should he have just said "find the velocity of block A with the dynamic equilibrium equations" instead of "vector method"? I don't understand why he would change terminology in the middle of a problem. Unless I am misunderstanding something here and the two are not related. This problem was my whole midterm by the way.

 

[haruspex]

Should he have just said "find the velocity of block A with the dynamic equilibrium equations" instead of "vector method"?

Probably, but you will have to ask him. His earlier mention of normal and tangential suggests he was somehow thinking it was a 2D problem.