question with unsure answer...?

Question

Three masses, M1= 2.5 kg, M2= 5.1 kg, and M3= 6.3 kg are made of the same material. They are on a horizontal surface and connected by massless strings. The system accelerates to the right at 2.37 m/s2 due to an external force F pulling on M3. Given that T1 is 10.61 N,
1- calculate the coefficient of kinetic friction mk.

my answer for this part is :
T1-f=M1*a
f=T-M1*a=10.61-(2.5*2.37)=4.685
N=M1*g=2.5*9.81=24.525
mk=f/N=4.685/24.525=0.191

2- Calculate the magnitude of the force F.
I'm not sure if my answer correct or not :

T2-T1=M2*a
T2=T1+M2*a=10.61+(5.1*2.37)=22.697N

F-T2=M3*a
F=M3*a+T2=(6.3*2.37)+22.697=37.628n

Answer 1

Your first part is correct. But I do not understand why you have committed mistake in second part. Does it mean that the first part you have not understood and just did it mechanically.

Why do you write: T1-f=M1*a? Because you think that there are two forces acting on mass M1. Please identify them. One by the string due to its tension and second due to the surface on which the M1 is being dragged. Now in the second case, when you consider the forces acting on M2, are they only due to T2 and T1! No the surface on which M2 is moving also applies a force called force of friction given by mk *N2. Write the equation corretly and then write the equation for the third mass also correctly and then solve you will get the answer and then I think you would not doubt it but be sure of it! If any query, Please do ask.