The tension in the rope is greater than 525 N, thus, the rope is in danger of breaking.
Acceleration of the bucket
The bucket started at rest, and after being lifted 3.0 m, it is moving at 3.0 m/s, the acceleration is calculated as follows;
v² = u² + 2as
v² = 0 + 2as
3² = 2(3)a
9 = 6a
9/6 = a
1.5 m/s² = a
Tension in the rope
T = m(a + g)
T = 50 (1.5 + 9.81)
T = 565.5
T ≈ 570 N
The tension in the rope is greater than 525 N, thus, the rope is in danger of breaking.
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