How Does Friction Affect the Motion of Three Blocks?

[complexc25]

You are given that the coefficient of kinetic friction between the block and the table in the figure is 0.560, and m1 = 0.150 kg and m2 = 0.250 kg.
(a) What should m3 be if the system is to move with a constant speed?

this is what i have:
T2 - T1 - f = m3a

m2g - m1g - ukg = m3
2.45 - 9.65 - 5.488 = 4.508kg

the answer is wrong, what is it that i am doing wrong?

 

[Doc Al]

this is what i have:
T2 - T1 - f = m3a

This is good.

m2g - m1g - ukg = m3
2.45 - 9.65 - 5.488 = 4.508kg

This is not good. For one thing, the tensions are not equal to the weights.

Hint: Apply Newton's 2nd law to each mass separately. You took care of M3, now come up with equations for M1 & M2.

You'll combine all three equations to solve for the acceleration and the tensions.

 

[complexc25]

i don't understand, i have for:
m1
T - m1g = m1a
m2
m2g - T = m2a

 

[Doc Al]

i don't understand, i have for:
m1
T - m1g = m1a
m2
m2g - T = m2a

Looks good, except that the tensions are different. Use T1 for m1 and T2 for m2.