How do I find the acceleration of a mass on a table?

[kasse]

[SOLVED] acceleration of mass on table

Homework Statement

http://www.badongo.com/pic/3633497

The Attempt at a Solution

The resultant force of the two hanging mases is 19.6 N. This means that just after the masses are released, the friction is 0.3*mg = 4.41 N, so that the total resultant force is 15.2 N.

The acceleration is then 15.2/1.5 = 10.1 m/s^2

Why am I wrong?

 

[Texag]

First of all, The coefficient of friction you have is for static friction.
Secondly, you must account for the entire system's mass since they are all accelerating.

 

[Dick]

You got an answer larger than 9.8m/s^2. That should be sending up alarms. No matter how heavy m3 is it's maximum acceleration down is 9.8m/s^2. Now try and do the problem right. There is a tension T1 and T2 in each of the two strings. You have to do a force balance for each mass and then set all of the accelerations equal.

 

[kasse]

I solved it in the same way, replacing the static coefficient with the dynamic, and replacing m₂ with (m₁+₂+₃). 1.9m/s^2. I don't know if my method is right, but it gave me the correct answer.

 

[Dick]

I solved it in the same way, replacing the static coefficient with the dynamic, and replacing m₂ with (m₁+₂+₃). 1.9m/s^2. I don't know if my method is right, but it gave me the correct answer.

That works. As Texag said, since everything is accelerating at the same rate, you can treat the system as one large mass and just add up the external forces. This does save you the step of dealing with the internal tensions.