Finding Maximum Angular Frequency and Tension on a Turntable

[Lanc1988]

Homework Statement

Two identical blocks are tied together with a string and placed along the same radius of a turntable that is spinning about its center. The inner block is 3 cm from the center and the outer block is 5 cm from the center. The coefficient of static friction between the turntable and the blocks is µs = 0.77, and the string is taut.

a) What is the maximum angular frequency such that neither block slides?
b) Now suppose that the blocks each have a mass m = 22 g. For the value of w you just found, what is the tension in the string?

Homework Equations

-T + µmg = m*R1*Theta^2
T + µmg = m*R2*Theta^2

The Attempt at a Solution

To get the answer to part a I used the above 2 equations and solved for theta which gave me w = 13.8 rads/sec. So to solve the for tension in the string I thought I could just plug in numbers for one of the equations and solve for T.. the problem is that each equation gives a different answer for T and they are both wrong. What am I doing wrong?

 

[Lanc1988]

anyone? I have been working on this last part of this problem for so long now.. I've tried about 10 different answers and they have all been wrong. When I click on help it tells me this:

Parts (a) and (b) really need to be solved together. Using your free-body diagram, apply F = ma to each block. Remember that the acceleration is the centripetal acceleration (which way is it pointed?). Following this procedure, you will find two equations and two unknowns (the angular frequency and the tension)

So I don't understand why I am able to solve those 2 equations I got for angular frequency but I can't solve them for the tension.. any ideas?

 

[Doc Al]

So to solve the for tension in the string I thought I could just plug in numbers for one of the equations and solve for T.. the problem is that each equation gives a different answer for T and they are both wrong. What am I doing wrong?

Redo your calculations for T. If you got different answers from each equation, you made a math error somewhere.

 

[Lanc1988]

are the equations right then? when i solved for theta in the equations I did it by adding them together.. to solve for T would I solve the first one for T and then plug that value into the second one for T.. but if I do that then the T's go away which is what is confusing me...

 

[Doc Al]

are the equations right then?

Yes. (What you call "theta" is the angular speed, usually called "omega".)

when i solved for theta in the equations I did it by adding them together..

Sure. No problem. That eliminates T and let's you solve for the angular speed.

to solve for T would I solve the first one for T

You could use either equation to solve for T. You'll get the same answer. (Try it and see.)

and then plug that value into the second one for T.. but if I do that then the T's go away which is what is confusing me...

Not sure what you mean here. You might be mixing yourself up a bit. You would plug the angular speed into either of your two equations to solve for T.

 

[Lanc1988]

ok.. so the equations are:
-T + µmg = m*R1*Theta^2
T + µmg = m*R2*Theta^2

so:
-T + (0.77)(22)(9.81) = (22)(0.03)(13.8)^2 so T = 40.491
T + (0.77)(22)(9.81) = (22)(0.05)(13.8)^2 so T = 43.302

this is very confusing to me.. you said my equations are right so apparently i must be putting in a wrong number..

 

[Doc Al]

Probably just round-off error. Calculate the value of "theta" to more digits and your two answers will be closer. (Also, the mass is given in grams.)

 

[Lanc1988]

im not sure what you mean by the mass is given in grams.. should it be converted to kg?

 

[Doc Al]

im not sure what you mean by the mass is given in grams.. should it be converted to kg?

Yes, if you want the tension in Newtons.

 

[Lanc1988]

ok.. got the answer right now. thanks for all your help! :)