Three objects are connected by light strings as shown in the figure below. The string connecting the $m_1=4\mathrm{.}65-kg$ object and the $m_2=4\mathrm{.}05-kg$ object passes over a light frictionless pulley.

$($a$)$ Determine the acceleration of each object. $($Enter the magnitudes in $\frac{m}{s^2}.)$

object magnitude

$m_1,$ Your response is within $10\%$ of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four$-$digit accuracy to minimize roundoff error. $\frac{m}{s^2}$

object direction

$m_1$

object magnitude

$\frac{m}{s^2}$

$m_2$

object direction

$m_2$

object magnitude

$\frac{m}{s^2}$

$m_3$

object direction

$m_3$

$($b$)$ Determine the tension in the two strings. $($Enter your answers in N$.)$

string between $m_1$ and $m_2$

Your response differs from the correct answer by more than $10\%.$ Double check your calculations. N

string between $m_2$ and the $3\mathrm{.}00$ kg object

Your response differs from the correct answer by more than $10\%.$ Double check your