Final answer:
The acceleration of a system with multiple masses connected by a light string over a frictionless pulley can be determined by considering the net force on the system. The tensions in the strings can be found by considering the forces acting on each mass individually.
Step-by-step explanation:
In a system with multiple masses connected by a light string over a frictionless pulley, the acceleration of the system can be determined by considering the net force on the system. If we denote the masses as m1, m2, and m3, and the tensions in the strings as T1 and T2, then the net force on the system is given by:
(m1 - m3)g = (m1 + m2 + m3)a
Where g is acceleration due to gravity. From this equation, we can solve for the acceleration of the system:
a = (m1 - m3)g / (m1 + m2 + m3)
The tensions in the strings can be found by considering the forces acting on each mass individually. For m1, the tension T1 pulls it upwards, and the tension T2 pulls it downwards due to the pulley. So we have:
T1 - T2 = m1a
Using these equations, we can find the acceleration and tensions in the system.