# Block Tension question

1. Nov 3, 2009

### candykane91

1. The problem statement, all variables and given/known data
The coefficient of kinetic friction between the 2.0 kg block in figure and the table is 0.350.

What is the acceleration of the 2.0 kg block?

2. Relevant equations
F=uK*Force Normal
Fnet=ma

3. The attempt at a solution
I tried to take the mass's of both the hanging and used them to calculate a net force on the block in the center and then solved for acceleration that way. Here's my work.

3kg*9.8=29.4N Right Side Tension
1kg*9.8=9.8N Left Side Tension
2kg*9.8=19.6N Force Normal

F=.35*19.6N
6.86N

(29.4N-6.86N)-9.8N=2kg*acceleration

a=6.34m/s^2

https://www.physicsforums.com/attachment.php?attachmentid=15777&d=1223407287

2. Nov 3, 2009

anyone???

3. Nov 4, 2009

### PhanthomJay

you are assuming that the tension is equal to the weight. That is true only if the system is not accelearting. This one is accelerating, so you must use free body diagrams of each block and apply Newton's 2nd and 3rd law.
OK
isolate each block and solve 3 equations with 3 unknowns.

4. Nov 4, 2009

### jmm

I've got the same question.

I've got these three equations:

m1*a = T1 - m1*g
m2*a = T3 - T1 - μ*m2*g
m3*a = m3*g - T3

Are those right? Solving for a using the first and second equations a=(g(m3-m1))/(m3+m1) which gives a=4.9 which would be the acceleration of the system if the centre mass wasn't there.

Using that value in the net force equation Fnet = m3(g-a) - m1(g+a) - μ*m2*g gives Fnet=6.86. Solving Fnet=ma for a gives you a=3.43 which is not right the right answer.

Can anyone tell me where I went wrong? Thanks!

5. Nov 4, 2009

### PhanthomJay

Looks OK, although the acceleration is likely to be in the other direction.
looks like you cancelled out T1 and T3, in error, using equations 1 and 3. T1 and T3 are not equal
This is not true. Correct your method of solving the 3 equations with 3 unknowns.

6. Nov 4, 2009

### candykane91

are you by any chance doing mastering physics?

7. Nov 4, 2009

### jmm

Ahh you're a life saver. Thanks a bundle!

I sure am. Combine those three equations I posted and you'll get the right answer.

8. Nov 4, 2009

### candykane91

ok. and btw who is this? are you going to u of c? physics 211 or 221?. the anser i got was 32 but i dunt think thats right. I used the 1st and 2nd equations to get T1 and T3 and plugged them into the 2nd equation. can u tell me wat i did wrong?

Last edited: Nov 4, 2009
9. Nov 4, 2009

### candykane91

ok now i got 8.2 as in answer. is that right?