Question

One 3.1 kg paint bucket is hanging by a massless cord from another 3.1 kg paint bucket, also hanging by a massless cord, as shown below.

If the two buckets are pulled upward with an acceleration of 1.30 m/s2 by the upper cord, calculate the tension in each cord.(lower cord) N(upper cord) N

Answer 1

Lower cord:
`T_1=34.4N`

Upper cord:
`T_2=68.8N`

Step-by-step explanation:

Both buckets, of mass
`m=3.1kg`, experiment an acceleration
`a=1.3m/s^2`. If the cord between them is under a tension
`T_1` and the upper cord is under a tension
`T_2`, then the equation for the lower bucket is
`ma=T_1-mg`, and for the upper bucket is
`ma=T_2-mg-T_1`, where we have just written all the forces on each bucket, and taken the upwards direction as positive. We can rewrite this as:

`T_1=ma+mg=m(a+g)`

`T_2=ma+mg+T_1=m(a+g)+m(a+g)=2m(a+g)`

And with our values we have:

`T_1=m(a+g)=(3.1kg)(1.3m/s^2+9.8m/s^2)=34.4N`

`T_2=2m(a+g)=2(3.1kg)(1.3m/s^2+9.8m/s^2)=68.8N`