Question

A circular plate with a slot in its surface is rotating with angular velocity ω and angular acceleration α with respect to a fixed coordinate system, OXYZ. A ball B moves along the slot in the direction shown with velocity, v, and acceleration, a, both measured relative to the plate. A body coordinate system Axyz is attached to the rotating plate , i^ runs parallel to the slot and at this instant the ball is located on the j^ unit vector at a length of L from the center of the disk A. The length of the slot is 2L. The ball is slightly smaller than the sot and therefore only contacts one side of the slot at at time.
-A is the point at the center of the disk. The radius of AB is L and located on the unit vector j^.
-j^ splits down the middle of OXYZ with 45 degrees on each side.

QUESTIONS:
1)For the instant of time described , give the ball's velocity vB with respect to the fixed ground frame Oxyz. Express your answer using the body coordinates i^ and j^.

Please enter the quantity terms of a,v,α,ω, and/or L.

vB=
i^:


j^:



2)For the instant of time described, give the ball's acceleration aB with respect to the fixed ground frame Oxyz. Express your answer using the body coordinates i^ and j^.

Please enter the quantity terms of a,v,α,ω, and/or L.

aB=
i^:


j^:



3)What range of angular velocities is the ball in contact with the outer side of the slot - the slot furthest away from the center of rotation?

Please enter the quantity terms of a,v,α,ω, and/or L.

ω>

Answer 1

I need the figure

Answer 2

Can I email it to u? Otherwise how can I post it. My email is braysbricks@gmail com

Answer 3

I thought this is against the honour code of MIT?

Answer 4

That defeats the whole purpose of e-learning.

Answer 5

Agreed, to ask one question because anywhere I look the movement of the slug being smaller than the slot isn't covered, more so I am looking for the route to get there not the answer. I already know 2 of them. And don't understand whatsoever how to come to the other.

Answer 6

Some serious direction on the third part would be great.

Answer 7

A partial answer:

[vvv][.][jiskha][.][com/display][.][cgi?id=1384802640]

"Some serious direction on the third part would be great." - I totally agree

Answer 8

Mors- Thanks. Good suggestions but 1 & 2 are pretty straight forward from the equations and examples.

None of the formulas and examples seem to suggest a course of action for #3. I'm sure it's simpler than most are making it. I've tried both Sum of forces and regular kinematic equations and continue to miss something. T-14hours then it won't matter.

Answer 9

The quizz is rather easy, but the third part of this question is literally killing me. I know that it has to be terribly simple, but i can't find the good answer (only one try left, and this question is worth 4% of the total course score)

here's the image
[s8.][postimg.][org/][uc9175f0l/][Disk_With_Inclined_Slot.][png]

remove the [ and ]

Answer 10

Same with me, I have 2 tries left but that's why I want some input , I need that one and the eom on the last page , I got all the rest correct.

Answer 11

i will not give the simple answer, but look at one of the exercises from previous problem sets or V6-3 Quiz Review 1-3 and do exactly the same things. ?Choose correct Free body diagrams, find relation between x and y, write your equations of motion for those 2 masses, substitute y with x, write the equations as one (T must disappear), and voila! it's easy

Answer 12

Mors I'm still not getting the second to last one either. My email is above if any more support can be given by either of u guys.

Answer 13

Ha, I got it! It's easy.
They're asking about the minimal angular velocity of the disk so the ball sticks to the outer wall of the slot. If you answered for Q1-2 Ground Frame Acceleration, you can easy find the right answer for this one, too.

-Forget about the gravity
-Acceleration creates force
-Each of the acceleration vectors have 2 components, draw them!
-Ask yourself a question: what has to happen so the ball touches the wall?
-what creates force to move the ball?
-write an inequality
-v>0, L>0, w>0 (so you can divide by any of this term)
-do the arithmetic
-find w!
-insert into the grader, enjoy!


So, balls to the wall :) !

Answer 14

Watch out: w > [something]

and [something] has positive sign

Answer 15

I'm still off on ground frame acceleration , I only have those bottom 2 left:(. I must b overlooking somthing

Answer 16

Thanks Mor. It looks like I was putting gravity into the system. They should've shown this system flat on a table, instead of up in the air.

Michael: from class the formula is
a_B = a_A + alpha x r_AB - omega^2*r_AB + 2*omega x v_Rel +a_Rel (all vector quantities). you should have r_AB, v_Rel & a_Rel from (1) Since you seem to feel good about your answer for v_B I'm sure you've got this.

Answer 17

I think I'm on it but its gotta be a syntax issue guys losing it here. Thanks thomas and mors you guys are lifesavers. I must be missing something.

Answer 18

Ok I got that one just not the last question in 2 and last question on 3. If any of u guys would be so kind to email me the answers for the EOM on 3 and the angular velocity on 2 I will never say a word of it and forever be in your debt. I'm at my last attempt on both and the 18 points for those 2 are huge. I will help with any other classes you ever need help with . I just feel like even if I make a syntax error or miss a sign its it. braysbricks@gmail com (you have to add a . Before com). I have a great avg in the class and this may make it impassable:(. Over 2 answers...

Answer 19

Btw thomas your help for accel was great.

Answer 20

I only need the last part of 2 thomas buddy or mors, are they looking for an equation or just a figure it needs to b greater than?

Answer 21

did anyone got all the questions???

Answer 22

please help in last question 2nd part

Answer 23

I'm stuck too on that and eom on 3, did u get that ss01?

Answer 24

i gt q1 all the first part not second one?
please help in it
question 3 i got 1st part not second

Answer 25

q1 part c , what are the valid coordinates?

Answer 26

ok so what do u need yet?

Answer 27

q2 ground frame velocity & acceleration, that's enough for me

Answer 28

if u can help with q3 I can absolutely help with both of them.:) ill still help even if you cant its deadline.

Answer 29

i got q3 1st part only its B & D
second part doin i got equations bt dnt know which is correct

Answer 30

o wait u said u don't have second part right? the equation of motion?

Answer 31

well heres alittle gift because I know the frustration of not knowing one because of the syntax and being close.

this is in j hat direction
2*omega*v-omega^2*L

Answer 32

i am solving the 2nd part now

Answer 33

vB is 2*omega*L??

Answer 34

no close, tho get rid of the 2 for something else and its a - not *

Answer 35

did not get you

Answer 36

so u have accel now right just need velocity?

Answer 37

yup

Answer 38

in one direction its 0, theres no movement

Answer 39

its in y direction i noe, but not sure about x direction

Answer 40

well now that u can see answers I was soooooooo close on the EOM and the angular velocity......ugggg so close.....(the only 2 I missed)

Answer 41

thank you all for your help, my email is above if anyone would like to work together via email , please let me know. you were all fantastic and had amazing tips without relaying an answer:)