A stone is tied to a string (length = 0.800 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 10.0% larger than the tension that exists when the circle is horizontal. Determine the speed of the stone.

Question

A stone is tied to a string (length = 0.800  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 10.0% larger than the tension that exists when the circle is horizontal. Determine the speed of the stone.

MathMate · Answer

Horizontal circle:
Centripetal force (horiz.)+weight of mass(vert.)
Tension on the string, Th
= √((mv²/2)²+(mg)²)

Vertical circle:
maximum tension is when the mass is at the bottom of the circle when the centripetal force is added to the weight.
Tension in the string, Tv
=mv²/2+mg

Equate Tv/Th=1.1
and solve for v.