# Blocks on turntable

1. Jul 14, 2005

### huskydc

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 = 0.79, and the string is taut.

-------------------------------------------------------------------------
What is the maximum angular frequency such that neither block slides?

2. Jul 14, 2005

### James R

How far have you got with this so far?

3. Jul 14, 2005

### huskydc

well, since i know what r and µ is, i was thinking about solving for velocity(tangential) first, but my question is that for r, do i account for two blocks' position?

that is, what should I use for r? the farthest block out (r =5cm)? i'm clueless with physics.

4. Jul 14, 2005

### Jelfish

The key is that neither block slides and the string is taught. That means you can take advantage of a balance of forces between the blocks and the table. Start by drawing the blocks from the side view and write down all the forces that you know are there. Then, you can start filling in forces because you know they must be balanced so that it doesn't move.

5. Jul 15, 2005

### huskydc

ok i got!!! if you're curious, i got omega = 13.12

Last edited: Jul 15, 2005
6. Jul 16, 2005

### Aki Yamaguchi

It would seem that husky and I are either in the same physics class, or using the same homework system. :) I'm still having trouble with this one (this and the accel plane are killing me).

This is my 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 2 cm from the center and the outer block is 6 cm from the center. The coefficient of static friction between the turntable and the blocks is µs = 0.8, and the string is taut.

What is the maximum angular frequency such that neither block slides?

-----
I think I'm just struggling with what the angular frequency actually IS. This is what I think I understand: when the turntable is rotating, the static friction force is pushing each block toward the center of the turntable. The tensions in the string between the two blocks point at each other:

[ 1 ] ---T---> ---- <---T--- [2]

I have no idea how to get started on this though. I'm not sure what I'm actually solving for.

Thank you so much!

A

Last edited: Jul 16, 2005
7. Jul 16, 2005

### Aki Yamaguchi

I've been working on this one again all morning. :\ In the vertical direction, the only forces are the normal force and the weight, which cancel each other out. In the horizontal direction, are the only two forces the static friction (pointing toward the center of the turntable for both blocks) and the tension (pointing outward for block 1 and inward for block 2)?

I know I need to set up 2 equations w/two unknowns, the angular frequency and the tension, but I'm not sure how to get started with that. I'm completely lost. :( I know when I find those equations and set them equal to ma, the a is the centripetal force, so a=v^2/r.

If the two equations are:

(block one) sigma F = T - f = ma
(block two) sigma F = -T - f = ma

How can I figure out what T and f are? I don't have the mass either. I think I'm missing something very key here. :(

A

8. Jul 16, 2005

### Pyrrhus

Try this approach for circular motion:

$$a_{radial} = R \dot{\theta}^{2}$$

so

$$\sum F_{x} = mR \dot{\theta}^{2}$$

From the FBDs you will have 2 unknowns and 2 equations, you can solve this.

9. Jul 16, 2005

### Aki Yamaguchi

What is the capital R in those equations?

I'm sorry. I'm so lost. :(

10. Jul 16, 2005

### Pyrrhus

R is for radius, i got a question does the string passes throught the centroid the turntable? or are the two block tied together such as the string doesn't pass throught the centroid of the turntable?

Last edited: Jul 16, 2005
11. Jul 16, 2005

### Aki Yamaguchi

Is R1 = 2, and R2 = 6, are those the two radii? I don't understand where I find the theta from for each equation, since I don't have an angle? I have it all drawn out on a whiteboard, but I think there's something I'm missing. Or is the theta in those equations the angular frequency, and thus what I'm supposed to find?

My roommate is digging out his old physics textbook for me, hoping it has a better definition of angular frequency. I think that's what I don't understand.

12. Jul 16, 2005

### Aki Yamaguchi

The string only connects the two blocks, it is not attached to the turntable in any way.

13. Jul 16, 2005

### Pyrrhus

Yes that theta is what you need to find.

inner block:

$$-T + \mu mg = mR_{1} \dot{\theta}^2 (1)$$

outer block:

$$T + \mu mg = mR_{2} \dot{\theta}^2 (2)$$

ok now add 1 and 2.

Last edited: Jul 16, 2005
14. Jul 16, 2005

### Pyrrhus

You know the arclength equation?

$$ds = R d \theta$$

Well when R is constant such as in the circular motion you can get

$$\frac{ds}{dt} = R \frac{d \theta}{dt}$$

$$v = R \dot{\theta}$$

where $\frac{d \theta}{dt} = \dot{\theta}$ is the angular speed also known as angular frequency (in oscillatory movements, vibrations)

for the normal component of acceleration:

$$a_{radial} = \frac{v^2}{R} = R \dot{\theta}^{2}$$

15. Jul 16, 2005

### Aki Yamaguchi

How can I get those masses to cancel out? I'm ending up w/three unknowns. Tension, mass, and theta. :\

16. Jul 16, 2005

### Jelfish

Did anyone confirm this? I actually got a different answer, 39.35 rad/sec.

17. Jul 16, 2005

### Pyrrhus

$$-T + \mu mg = mR_{1} \dot{\theta}^2 (1)$$

$$T + \mu mg = mR_{2} \dot{\theta}^2 (2)$$

$$2 \mu mg = mR_{1} \dot{\theta}^2 + mR_{2} \dot{\theta}^2$$

$$2 \mu g = R_{1} \dot{\theta}^2 + R_{2} \dot{\theta}^2$$

Last edited: Jul 16, 2005
18. Jul 16, 2005

### huskydc

hey aki, do you have a instant messenger or something, b/c i can walk you through it if you want.

19. Jul 16, 2005

### Jelfish

Don't forget about the friction force. That has a factor of m inside it. Get rid of the Tension by solving for T for both equations and setting them equal.

20. Jul 16, 2005

### OlderDan

The problem says the blocks are on the same radius, so the string is only on one side of center.

You might want to change your sign convention. The RHS of these equations are positive quantities, so the LHS of each equation should be net positive.