Math Help - Mechanics question

1. Mechanics question

Three bodies are connected by a light inextensible string passing over a smooth pulley. one mass lies on a horizontal surface (mass 10kg) and the others (4kg and 6kg) hang freely. With the strings taut it is released from rest. Fiind ensuing accelerations and the tension in the strings.

thanks any help is great

2. let $T_1$ = tension in the string between the surface mass and the hanging mass.
$T_2$ = tension in the string between the hanging mass.

I'll assume the 4kg mass is above the 6 kg mass.

net force equation for the surface mass (10 kg) ...

$T_1 = 10a$

net force equation for the 4 kg mass ...

$(T_2 + 4g) - T_1 = 4a$

net force equation for the 6 kg mass ...

$6g - T_2 = 6a$

solve the system of equations for $T_1$ , $T_2$, and " $a$" ... you should get $a = \frac{g}{2}$, $T_1 = 5g$ Newtons, and $T_2 = 3g$ Newtons.