The tension in the cable and the <em>net</em> acceleration of the block B are 291.814 newtons and 0.112 meters per square second, respectively.
<h3>How to determine the tension and the acceleration of block B</h3>
Based of the representation seen in the image, an <em>external</em> force moves the block A <em>downwards</em> and the block B moves <em>upwards</em> and with an net acceleration of same magnitude due to the cable. By Newton's laws we construct the free body diagrams for each mass and that can be seen in the image seen below.
The <em>motion</em> equations are described below:
Mass A
250 N - 0.4 · Na - T + (30 kg) · (9.807 m / s²) · sin 30° = (30 kg) · a (1)
Na - (30 kg) · (9.807 m / s²) · cos 30° = 0 (2)
Mass B
- T + 0.4 · Na + 0.3 · Nb + (15 kg) · (9.807 m / s²) · sin 30° = - (15 kg) · a (3)
Nb - Na - (15 kg) · (9.807 m / s²) · cos 30° = 0 (4)
By (2):
Na = (30 kg) · (9.807 m / s²) · cos 30°
Na = 254.793 N
By (4):
Nb = 254.793 N + (15 kg) · (9.807 m / s²) · cos 30°
Nb = 382.190 N
Then, we have the following system of <em>linear</em> equations:
T + (30 kg) · a = 250 N - 0.4 · Na + (30 kg) · (9.807 m / s²) · sin 30°
T + 30 · a = 295.188
T - (15 kg) · a = 0.4 · Na + 0.3 · Nb + (15 kg) · (9.807 m / s²) · sin 30°
T - 15 · a = 290.127
The solution of the <em>linear</em> system is T = 291.814 N and a = 0.112 m / s².
To learn more on Newton's laws: brainly.com/question/27573481
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