Coefficient of kinetic friction between the two blocks

[Squeezebox]

Homework Statement

The coefficient of kinetic friction between the two blocks is 0.30. The surface of the table and pulleys are frictionless.

m₁=2 kg
m₂=3 kg
m₃=10 kg

Homework Equations

$$\Sigma$$F=ma
T₂-m₃g=m₃a
T₁-T₂=m₂a
friction-T₁=m₁a

The Attempt at a Solution

T₂=m₃g+m₃a
T₁=friction-m₁a

friction-m₁a-m₃g-m₃a=m₂a

(friction-m₃g)/(m₁+m₂+m₃)=a
a=-6.15m/s²

The answer in my book say it is -5.7m/s², though.

 

[method_man]

Homework Statement

The coefficient of kinetic friction between the two blocks is 0.30. The surface of the table and pulleys are frictionless.

m₁=2 kg
m₂=3 kg
m₃=10 kg
The answer in my book say it is -5.7m/s², though.

T₂=m₃g-m₃a
T₁=m₁a+m₁gμ
T₂=T₁+m₁gμ+m₂a
a=(m₃g-m₁gμ-m₁gμ)/(m₁+m₂+m₃)=5.7552

 

[nlightner]

I would suggest double-checking your calculations and equations to ensure accuracy. It is also important to consider any assumptions that may have been made, such as the surfaces being perfectly smooth and the blocks being in a vacuum. Additionally, it may be helpful to show your work and explain your reasoning in more detail to better understand where the discrepancy in your answer may be coming from. It is also important to note that the coefficient of kinetic friction can vary depending on the materials and conditions involved, so it may be worth exploring any potential sources of error in your calculation.