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

Answer:

Lower cord: $T_1=34.4N$

Upper cord: $T_2=68.8N$

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:

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

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