Why Does My Friction Coefficient Calculation Differ from My Teacher's Answer?

[Maiia]

Homework Statement

Three blocks of masses 10kg, 5kg, and 3.090 kg are connected by light strings that pass over frictionless pulleys as shown. The acceleration of the 5kg block is 2m/s^2 to the left, and the surfaces are rough. Find the tensions in each string and the coefficient of friction btw the blocks and the surfaces assuming it is the same for both blocks.

Here is my picture and equations. I assumed that the acceleration would be 2 m/s^2 for all three blocks.

The issue I have is that no matter how many times I try the problem, I end up with a different friction coefficient than the answer my teacher gave me of 0.66. Can someone tell me what I'm doing wrong?

 

[jbsteele]

Homework Equations F=maT1-T2= m2*aT2-T3=m3*aThe Attempt at a Solution T1=10(2) =20NT2=5(2)-20=0NT3=3.090(2)=-6.18NFriction= (T1-T2)/(m1*a)Friction= (20-0)/(10*2)Friction= 2/20Friction= 0.1

 

[thomate1]

I would first commend the student for their efforts in attempting to solve the problem. It is important to note that different approaches and methods may yield different results, and it is important to carefully check all assumptions and calculations to ensure accuracy.

One possible explanation for the discrepancy in the calculated friction coefficient could be a mistake in the equations or calculations. I would suggest double-checking the equations and units used, and also considering any simplifications or assumptions made in the problem.

Another possibility could be experimental error or variations in the setup of the problem. In a real-world scenario, there may be slight differences in the surfaces or pulleys used, which could affect the friction coefficient. It is important to keep this in mind and understand that calculated values may not always match real-world values exactly.

In conclusion, it is important to carefully review and check all assumptions and calculations, and to consider any potential sources of error when solving problems in physics.