Maximizing Angular Frequency for Non-Sliding Blocks on a Turntable

[v3lox]

Hey guys I am having a hard time trying to solve this problem and I was hoping someone could help me out with it because to be honest I don't even have any idea how to start it.

Problem:
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 4 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 = 0.74, 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 = 35 g. For the value of w you just found, what is the tension in the string?

Any help is greatly appreciated!

 

[tiny-tim]

Welcome to PF!

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 4 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 = 0.74, 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 = 35 g. For the value of w you just found, what is the tension in the string?

Hi v3lox! Welcome to PF!

Let's start by working out which block will slide first …

Hint: the tension force on both blocks is equal and opposite … so which block, at any angular speed, has the higher friction force?

 

[v3lox]

well I've been looking around on other webpages to see if anyone else was having trouble with this same problem and i found a few of them and in the end i had written 2 equations with 2 unknowns

1) T - umg = m R1 w^2
2) -T - umg = m R2 w^2

i know that when i add them the tensions should cancel out but how would i solve for m since it is not given?

 

[tiny-tim]

sorry!

well I've been looking around on other webpages to see if anyone else was having trouble with this same problem and i found a few of them and in the end i had written 2 equations with 2 unknowns

1) T - umg = m R1 w^2
2) -T - umg = m R2 w^2

i know that when i add them the tensions should cancel out but how would i solve for m since it is not given?

Hi v3lox!

(have a mu: µ and an omega: ω and a squared: ² )

i] don't use the web! there are dozens of websites, but only a few mechanics equations, so just write out all the equations you know and then choose the ones that fit!

ii] I'm sorry … my last post was misleading … you don't need the tension until part b).

Since the blocks will slide outward, and they can't get any further apart, either the inner one slides first (and the tension is zero), or they both slide at the same time.

It's the latter (can you prove that? ), so to find ω you need to consider the forces on the two blocks as a single unit.

iii] m is given … its 35g !

(oh, and check the ± signs in your equations )

 

[v3lox]

yes i finally got it! :)
somehow i completely overlooked the mass given for some odd reason maybe i just thought that it would only apply for part b

after checking my signs and adding the two equations with the mass given ;) i came up with the right equation to solve for w and the rest was easy

thanks for your help tiny-tim really appreciate it! :)