Question

If the tension in the string in figure is $16N$ and the acceleration of each block is $0.5m/s^2$, find the friction coefficient at the two contacts with the blocks.

• A. The coefficient of friction $\left({\mu }_1\right)$ is $0.75$
• B. The coefficient of friction $\left({\mu }_2\right)$ is $0.06$
• C. The coefficient of friction $\left({\mu }_1\right)$ is $0.006$
• D. The coefficient of friction $\left({\mu }_2\right)$ is $0.75$

Answer 1

The correct option is A The coefficient of friction $\left({\mu }_1\right)$ is $0.75$

For $2kg$ block.

$\begin{array}{c}T-f_1=2a\\ \Rightarrow T-f_1=2\times 0.5\\ \Rightarrow 16-f_1=1\\ \Rightarrow f_1=15N\end{array}$

For $3kg$ block

$\begin{array}{c}4g\sin \theta -T-f_2=4a\\ \Rightarrow 20-16-f_2=2\\ \Rightarrow f_2=2N\\ \therefore f_1=15N\\ f_2=2N\end{array}$