Answer: We can use Newton's second law, which states that the net force acting on an object is equal to its mass multiplied by acceleration.
Let's call the acceleration of the system "a". Then the net force acting on m1 is T1 - T2 + m1 * a = 0.
The net force acting on m2 is T2 - m2 * a = 0.
And the net force acting on m3 is T2 + m3 * a = 0.
Solving these three equations, we get:
T1 = T2 + m2 * a = 60.0 N + 8.00 kg * a
m1 * a = -T2 + 60.0 N + m1 * a
m3 * a = T2 - 60.0 N + m3 * a
Substituting T2 = 60.0 N, we get:
T1 = 60.0 N + 8.00 kg * a
m1 * a = -60.0 N + 10.0 kg * a
m3 * a = 60.0 N + 12.0 kg * a
Solving for the acceleration, we get:
a = (60.0 N + 8.00 kg * a) / (10.0 kg - 8.00 kg) = (60.0 N + 8.00 kg * a) / 2.0 kg
a = (60.0 N + 8.00 kg * a) / 2.0 kg = (60.0 N) / 2.0 kg + (8.00 kg * a) / 2.0 kg
a * 2.0 kg = 60.0 N + 8.00 kg * a
a = 60.0 N / 2.0 kg + 8.00 kg * a / 2.0 kg
a * 2.0 kg - 8.00 kg * a = 60.0 N
a * 10.0 kg = 60.0 N + 8.00 kg * a
a = 60.0 N / 10.0 kg = 6.0 m/s²
Finally, we can use T1 = 60.0 N + 8.00 kg * a to find T1:
T1 = 60.0 N + 8.00 kg * 6.0 m/s² = 60.0 N + 48.0 N = 108.0 N
So the acceleration of the masses is 6.0 m/s², and the tension T1 is 108.0 N.
Step-by-step explanation: