Vehicle Travelling up a Cylinder

[hartmac4]

Sorry, first time using this site.



I was looking for help with the above problem. I'm not so concerned with solving part b, but more just finding the right equations for part a.

If there is an equation editor for this site, let me know.

I know z=(h*theta)/(2*pi), and I know the below equations from the notes, where e_R, e_theta, and k are the cylindrical coordinates.

r(t) = R*e_R + z*k
v(t) = R'*e_R + R*(theta')*e_theta + z'*k
a(t) = (R''-R*theta'^2)*e_R + (R*theta'' + 2*R'*theta')*e_theta + z''*k

The problem is, I don't know a second equation that relates theta (or z) to the known values (m, R, and h). In the similar example problem, they had two equations they used to relate the knowns to z and theta (attached below).



Any help figuring this part of the problem out would be appreciated!

 

[Deleted member 4993]

Cylindrical Dynamics

Sorry, first time using this site.

View attachment 8411

I was looking for help with the above problem. I'm not so concerned with solving part b, but more just finding the right equations for part a.

If there is an equation editor for this site, let me know.

I know z=(h*theta)/(2*pi), and I know the below equations from the notes, where e_R, e_theta, and k are the cylindrical coordinates.

r(t) = R*e_R + z*k
v(t) = R'*e_R + R*(theta')*e_theta + z'*k
a(t) = (R''-R*theta'^2)*e_R + (R*theta'' + 2*R'*theta')*e_theta + z''*k

The problem is, I don't know a second equation that relates theta (or z) to the known values (m, R, and h). In the similar example problem, they had two equations they used to relate the knowns to z and theta (attached below).

View attachment 8412

Any help figuring this part of the problem out would be appreciated!

Locate your origin - using the description.

Locate the starting point 0f the car on the cylinder - using the description.

Θo is the line joining the origin to the starting point.

So at the starting point - |r| = R, Θ = 0 & z = 0

In dynamics, the hardest part is to read the problem carefully and extract the initial/final conditions.

 

[hartmac4]

Starting Point

Thanks. I already know that the starting point conditions, but that doesn't seem to help me get closer to finding r(t) or its derivatives. Care to elaborate a little further.

 

[hartmac4]

Unsure of How to Use This

Locate your origin - using the description.

Locate the starting point 0f the car on the cylinder - using the description.

Θo is the line joining the origin to the starting point.

So at the starting point - |r| = R, Θ = 0 & z = 0

In dynamics, the hardest part is to read the problem carefully and extract the initial/final conditions.

My reply never seemed to post. Anyways, I already had the final and initial condition written down, but I'm not sure how to use this information to proceed. Can you elaborate a little more?

 

[stapel]

In the similar example problem, they had two equations they used to relate the knowns to z and theta (attached below).

View attachment 8412

Do you understanding the solution to this related example? If so, how have you tried to apply it? If not, where does it stop making sense?

Thank you!

 

[Deleted member 4993]

My reply never seemed to post. Anyways, I already had the final and initial condition written down, but I'm not sure how to use this information to proceed. Can you elaborate a little more?

What was your final r(t)?

 

[hartmac4]

Solved It

So, I talked to the professor. He wants the problem solved in terms of theta and theta_dot. Makes the problem really easy. Just wish he would have said what variables to keep in the final solution. If anyone is interested, I can post the solution.

 

[mmm4444bot]

If anyone is interested, I can post the solution.

Yes, we like to see student work. It's also probable that some future readers of this thread will be interested, too.

My reply never seemed to post.

New members' first three posts must wait for approval. (This is for SPAM-control.) You were supposed to have been advised of this policy by e-mail and by private message, when you joined the forum.

 

[mmm4444bot]

If there is an equation editor for this site, let me know.

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