Question

A stone is tied to a string (length = 0.880 m) and whirled in a circle at the same constant speed in two different ways. First, the circle is horizontal and the string is nearly parallel to the ground. Next, the circle is vertical. In the vertical case the maximum tension in the string is 14.0% larger than the tension that exists when the circle is horizontal. Determine the speed of the stone.

Answer 1

Hello Buddy!

Here is the required solution!

It is Important to understand that when the stone is whirled around a path which is horizontal to the earth's surface, then the stone only experiences a centripetal force.

However, when then stone is whilred in a vertical circle, then there would be an increased acceleration caused by gravity whenever the stone goes down. This is denoted by 'g'.

SOLUTION

As said earlier, This additional maximum tension on the rope is a result of 'g' and is the value given as 14%.

Thus, a1 + g = a2

where, a1 = acceletation 1, a2=acceleration 2, g=9.8 m/s²

9.81 + a1 = 0.14 a1

This gives us a1 = =

Thus, v =

Thus the answer comes out to be 8.30662 m/s

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