Answer:
The acceleration of the system is 1.02 m/s^2 upward, and the tension in the string is 40.596 N.
Step-by-step explanation:
In this system, the two masses are connected by a string that passes over a frictionless pulley, so they are effectively connected and move together. Since the system is vertical, we can use the force of gravity as the only force acting on the masses.
Let's call the acceleration of the system "a", and let's assume that the positive direction is upward. Then we can write the following equations of motion for each mass:
For the 5.2 kg mass:
T - m1g = m1a
For the 4.8 kg mass:
m2g - T = m2a
where T is the tension in the string, m1 and m2 are the masses, g is the acceleration due to gravity (9.81 m/s^2), and a is the acceleration of the system.
Since the two masses are connected by a string, their accelerations are equal and opposite in direction, so we can write:
a = -m2a
Substituting this into the equation for the 5.2 kg mass, we get:
T - m1g = -m2a
Substituting in the values, we get:
T - (5.2 kg)(9.81 m/s^2) = -(4.8 kg)a
Similarly, substituting this into the equation for the 4.8 kg mass, we get:
(4.8 kg)(9.81 m/s^2) - T = (5.2 kg)(-a)
Simplifying both equations, we get:
T = 40.596 N
a = 1.02 m/s^2