# 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?

Nov 12, 2015

$245 \text{N}$ on the lower cord and $735 \text{N}$ on the upper cord.

#### Explanation:

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.

$F = m g$

Here, $m$ is the mass of the bucket and $g$ is the acceleration due to gravity. The bottom bucket therefore weighs;

F_l = (25"kg")(9.8 "m/s"^2)=245"N"

So there is $245 \text{N}$ of tension on the lower cord. The top cord, however, is holding the weight of both buckets, so next we need to find the weight of the upper bucket and add it to the weight of the lower. Using Newton's second law again, the weight of the upper bucket is;

F_u = (50"kg")(9.8 "m/s") = 490 "N"

The total weight on the upper cord is the sum of the weights of the two paint cans.

${F}_{t} = {F}_{l} + {F}_{u} = 245 \text{N" + 490"N" = 735"N}$