Buckets and a Pulley Two buckets of sand hang from opposite ends of a rope that passes over an ideal pulley. One bucket is full and weighs 120 N ; the other bucket is only partly filled and weighs 70 N .
Part A: Initially, you hold onto the lighter bucket to keep it from moving. What is the tension in the rope?
Part B: You release the lighter bucket and the heavier one descends. What is the tension in the rope now?
Part C: Eventually the heavier bucket lands and the two buckets come to rest. What is the tension in the rope now?

Since, the lighter bucket is supported by my had. So, the only unbalanced force in the system is the weight of heavier bucket. Hence, the tension in rope will be equal to the weight of heavier bucket.

T = 120 N

Part B:

This is the case where, two masses hang vertically on both sides of the pulley. To find the tension in such case we have the formula:

T = (2 m₁m₂g)/(m₁+m₂)

where,

m₁ = mass of heavier object = W₁/g = (120 N)/(9.8 m/s²) = 12.24 kg

m₁ = mass of lighter object = W₂/g = (70 N)/(9.8 m/s²) = 7.14 kg

g = 9.8 m/s²

Therefore,

T = [(2)(12.24 kg)(7.14 kg)(9.8 m/s²)]/(12.24kg + 7.14 kg)

T = 1713.6 N.kg/19.38 kg

T = 88.42 N

Part C:

Since, the heavier bucket is on ground. So, its weight is balanced by the normal reaction of the ground. The only unbalanced force in the system is the weight of lighter bucket. Hence, the tension in rope will be equal to the weight of lighter bucket.

T = 70 N