# Math Help - Calculating Tension

1. ## Calculating Tension

Hi, I'm trying to do this physics problem, but I just can't seem to figure out how to do this problem involving tension. I think it has something to do with adding the masses together on either side of Tc, but I can't seem to come up with the correct answer.
Any help is greatly appreciated, thanks!

2. Originally Posted by vesperka
Hi, I'm trying to do this physics problem, but I just can't seem to figure out how to do this problem involving tension. I think it has something to do with adding the masses together on either side of Tc, but I can't seem to come up with the correct answer.
Any help is greatly appreciated, thanks!
Assuming that the strings are inextensible (and I guess they will be if they're massless ha ha), the simplest approach is:

Start off by considering the four masses as a single system under a net force of 27 newton to the left. Then the acceleration of the system is 3 m/s^2 to the left.

Now consider the net force on the 5 kg mass. Keep in mind that it has an acceleration of 3 m/s^2 to the left .....

3. So using F=ma, I could plug in a=3 and m=5 to get Tc=15N?
Or would I plug in a mass of 4kg to get Tc=12N?
Thanks for the help, I think I'm starting to understand it now.

4. Originally Posted by vesperka
So using F=ma, I could plug in a=3 and m=5 to get Tc=15N?
Or would I plug in a mass of 4kg to get Tc=12N?
[snip]
No and no!!

Take left as the positive direction. Then the net force on the 5 kg mass is $T_c - 14$ newton.

But net force = (mass)(acceleration) = (5)(3) = 15 newton.

Therefore .....

5. So I would add 15N to the 14N to get 29N? Is that correct?

6. Originally Posted by vesperka
So I would add 15N to the 14N to get 29N? Is that correct?
Hmmm lessee now ..... $T_c - 14 = 15 \therefore T_c = ......$ by Jove, you're right!!

7. Thanks for the help!