Final answer:
The acceleration of the system is approximately 0.39 m/s², and the tension in the cord on the left and right are approximately 61 N and 85 N respectively.
Step-by-step explanation:
First, we need to determine the net force acting on the system. The mass of the blocks are 6.0 kg, 9.0 kg, and 10 kg respectively. The force of friction between the table and the 10 kg block can be calculated by multiplying the coefficient of friction (0.20) by the weight of the block (10 kg * 9.8 m/s²). By setting up the equations of motion using Newton's second law, we can determine the acceleration of the system.
(a) To find the acceleration, we need to sum up the forces acting on the system.
Net force = Sum of all forces
= (T1 - Ffriction) + (T2 - Ffriction)
Net force = (T1 - 19.6 N) + (T2 - 19.6 N)
Net force = T1 + T2 - 39.2 N
Since the blocks are connected, they have the same acceleration.
T1 = T2
Hence, Net force = 2T1 - 39.2 N
Using Newton's second law, Net force = mass * acceleration, we can set up the equation:
2T1 - 39.2 N = (6.0 kg + 9.0 kg + 10 kg) * acceleration
2T1 - 39.2 N = (25.0 kg) * acceleration
T1 = (25.0 kg * acceleration + 39.2 N) / 2
Substituting T1 = T2 and T1 = (25.0 kg * acceleration + 39.2 N) / 2, we can solve for the acceleration:
2T1 - 39.2 N = 25.0 kg * acceleration
(25.0 kg * acceleration + 39.2 N) - 39.2 N = 25.0 kg * acceleration
25.0 kg * acceleration = 39.2 N
acceleration = 39.2 N / 25.0 kg
acceleration ≈ 1.568 m/s²
(b) To find the tension in the cords, we can substitute the calculated acceleration (1.568 m/s²) back into the equation T1 = (25.0 kg * acceleration + 39.2 N) / 2:
T1 = (25.0 kg * 1.568 m/s² + 39.2 N) / 2
T1 ≈ 61 N
Since T1 = T2, the tension in the cord on the right is approximately 61 N.