Question

The small ball of mass m and its supporting wire become a simple pendulum when the horizontal cord is severed. Determine the ratio k of the tension T in the supporting wire immediately after the cord is cut to that in the wire before the cord is cut.

Answer 1

See the attached image and the explanation below

Step-by-step explanation:

We must draw a schematic of the described problem, after the sketch it is necessary to make a free body diagram, at the time before and after cutting the cord.

These free body diagrams can be seen in the attached image.

First we perform a sum of forces on the x & y axes before cutting the cord, to be able to find the T tension of the wire. (This analysis can be seen in the attached image).

In this way we get the T-wire tension equation, before cutting.

Now we make another free body diagram, for the moment when the wire is cut (see in the attached diagram).

It is important to clarify that when the cord is cut, the system will no longer be in statically, therefore newton's second law will be used for summation of forces which will be equal to the product of mass by acceleration.

Finally with equations 1 and 2 we can find the K ratio.