A 25 Kg paint bucket is hanging by a massless cord from another 50 kg paint bucket also hanging by a massless cord. If the buckets are at rest, what is the tension in each cord?
Its typically helpful to start with a diagram.
Gravity is supplying the force in this problem. That means that the tension on the strings will be equal to the weight of the paint buckets. Since the lower string is pulling on the upper string, lets start with the lower cord.
Since the two buckets are stationary, the tension on this cord only depends on the weight of the bottom bucket. We can calculate the weight of the bucket using Newton's second law, adapted for gravity.
So there is
The total weight on the upper cord is the sum of the weights of the two paint cans.