Tension Along Rope with Masses

[zaper]

I've worked through this problem a few different ways now and each one gives me different answers and I am looking for some guidance as to which is correct:

Four blocks of mass m1=1kg, m2=2kg, m3=3kg (very original right?), and unknown mass m4 are on a frictionless surface (pic attached). Force Fl pulls in the left direction at 30N and Fr to the right at 50N. The tension between m2 and m3 is 36N. What is m4?

As I worked through the problem I labeled all tensions as shown in the picture. I know T1=30N and T5=50N. My biggest problem arises from whether T3=36N or if 2*T3=36N.

The first time I did this problem I used 2*T3-36N or T3=18N. Then using Newton's 2nd law I set up the equations T2-T1=m1*a, T3-T2=m2*a, and so forth. Using this method I got that a=4m/s2 to the right and m4=5kg.

The second time I did this I used T3=36N and using the same equation setup as before I got a=2m/s2 to the left which seemed plausible, however using T5-T4=m4*a I ended up with m4=-10kg which seems not so plausible.

Any suggestions?

 

[technician]

T3 = 36N not 2x36N... it is pulling with 36N to the right on the combination (m1+m2) and pulling with 36N to the left on the combination (m3+m4)
You are given the tension between m2 and m3 to be 36N so (m1+m2) experience a resultant force to the right of what?... can you see that and calculate the acceleration of (m1 and m2).
Once you know the acceleration you can apply resultant force on (m3+m4) to calculate m4

 

[zaper]

So since m1+m2=3kg and the experience a force of 6N then a=2.

Then m3 and m4 experience 14N so

14=(m3+m4)*2 => 14=6+2*m4 => 8=2*m4 => 4kg=m4?

Is that right?

 

[technician]

that is exactly what I got

 

[asteriatic]

It seems like you have approached the problem correctly, but there may be a mistake in your calculations. Here are a few things to check:

1. Make sure you are using the correct signs for the tensions. The tension T3 should be pointing to the right, since it is pulling on a mass to the right. This means that T3 should be positive in your equations.

2. Double check your equations to make sure you are using the correct masses and accelerations. For example, when setting up the equation T3-T2=m2*a, make sure you are using the correct mass for m2 and the correct acceleration for the system.

3. It may be helpful to draw a free body diagram for each block to visually represent the forces acting on it. This can help you keep track of the correct signs and values for each tension.

4. If you are still getting conflicting answers, try solving the problem using a different method or approach to see if you get the same result. Double checking your work and trying different methods can help you identify any errors or mistakes.

Overall, the most important thing is to carefully check your work and make sure you are using the correct values and signs for each tension. Good luck!