physics help plz
posted by emma .
One 3.5 kg paint bucket is hanging by a massless cord from another 3.5kg paint bucket, also hanging by a massless cord, as shown in the figure .
Part a) If the buckets are at rest, what is the tension in lower and higher cord ?
Part b)If the two buckets are pulled upward with an acceleration of 1.55 by the upper cord, calculate the tension in the lower cord and upper cord

(a) When the buckets are at rest, the tension in the cords just equal the weight that is suspended beneath them.
Each bucket weighs
m•g = 3.5• 9.8 = 34.3 N.
The lower bucket has gravity down of 34.3 N and the tension (T) in the lower string up, the acceleration is 0, so the Second Law F = ma looks like:
T – m•g = 0,
T =34.3 N.
The top bucket has the tension in the cord above it (T) the force of gravity of 34.3 N down and the tension of the lower string of 34.3 N downward on it. The acceleration of it is zero, so Second Law F = ma looks like:
T – 34.3 – 34.3 = 0,
T = 68 N.
(b)
When the buckets are at accelerating at 1.55 m/s² upwards, the tensions in the cord are more than the weight below them.
The lower bucket has gravity down of 34.3 N and the tension (T) in the lower string up and an upward acceleration of 1.55 m/s², so F = ma looks like:
T  m•g = m•a,
T =m•a+m•g = m• (a+g) = 3.5•(1.55+9.8) = 39.73N.
The upper bucket has its own weight of 34.3 N down and the tension in the upper string (T) up, and the tension in the lower string of 39.73N down. It has an upward acceleration of 1.55 m/s², so F = ma looks like:
T – 34.3 – 39.73 = ma,
T = 34.3+39.73+3•1.55 =78.68 N.