# Pulley/tension problem

1. May 12, 2015

### cdenne

1. The problem statement, all variables and given/known data
I have a problem about two masses: m1 sitting on a table and m2 hanging off the end of th table across a frictionless pulley. There is friction between m1 and the table, however. The system is released from rest and m2 falls 1 meter in 1.2 seconds. m1=10.0 kg, m2=5.00 kg. find the coefficient of kinetic friction.

2. Relevant equations
I used x=.5at^2 to find a. I used m2g - T = m2a for m2 with down being positive and up being negative. And I used T - (mu)m1g = m1a for m1 with positive being the direction toward the end of the table.

3. The attempt at a solution
I used x=1 meter, t = 1.2 seconds in the first equation and solved for a to get a = 1.39 m/s^2. Then I solved the next two equations for T, set them equal to each other, then solved for mu to get mu = (m2g - m2a - m1a) / (m1g). This gave me a negative value for mu (-0.163) and I know that mu should be positive. Thanks for your help.

2. May 12, 2015

### Staff: Mentor

Please show your arithmetic for this: mu = (m2g - m2a - m1a) / (m1g)

Chet

3. May 13, 2015

### ME_student

Lets see some FBD's first.

4. May 13, 2015

### Staff: Mentor

He obviously used some correct FBDs, or he couldn't have written down the two force balance equations correctly.

Chet

5. May 13, 2015

### cdenne

(5*9.8 - 5*1.39 - 10*1.39) / (10*9.8) = - 0.163

Alright. I just found my mistake. I don't know what I did on the calculator last night, but I kept getting -0.163. Now I get the correct value of 0.287. Thanks for your help. By the way, what are FBDs?

6. May 13, 2015

### Staff: Mentor

Free Body Diagrams. You obviously used these to get your force balances.

Chet

7. May 13, 2015

### cdenne

Thank you very much for your help.

8. May 17, 2015

### ME_student

OP didn't know what a FBD was so I was going to start helping him/her by having him/her draw some FBD. BTW Mr. Chet if he used correct FBD's he wouldn't be here asking us questions. Obviously OP must have analyzed something wrong on his/her free body diagram.

9. May 17, 2015

### Staff: Mentor

Dear ME_student,

I stand by what I said, to wit: If he hadn't drawn proper free body diagrams, he would not have been able to write down the force balance equations correctly (which he was able to do). His difficulty was not in drawing free body diagrams and developing the force balance equations, but in solving the force balance equations. So, obviously OP must not have analyzed something wrong on his/her free body diagram. Based on 50 years of engineering experience, this is the determination that I made. When you have 50 years of experience, come back and we can discuss this further. In the meantime, this thread is Closed.

If you want to discuss the issue further, you can contact me via private conversation. But be advised that, as a Mentor, I'm beginning to get an itchy Warning finger.

Chet