Question

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

Answer 1

(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.