A stone is tied to a string (length L = 1.10 m) and whirled in a circle at the s

Question

A stone is tied to a string (length L = 1.10 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 15.0% larger than the tension that exists when the circle is horizontal.

Remember that the centripetal force is the vector sum of the radial forces. Both of the forces in the free-body diagram are radial. The tension points in toward the center of the circular motion, and the weight points away from the center.

Write an expression for the centripetal force on the stone in terms of the forces in the free body diagram in Step 6, when the stone is moving on the vertical circle at Position 3.

Remember that the centripetal force is the vector sum of the radial forces. Both of the forces in the free-body diagram are radial. The tension points in toward the center of the circular motion, and the weight points away from the center.

Explanation / Answer

If the circle is horizontal, Tension

T = mv^2/ r
If the circle is vertical, at the lowest position
T is the maximum and

Tmax = mv^2 /r +mg

since this is 15% greater than mv^2/r,

1.15 mv^2/r = mv^2/r + mg

1.15 v^2/r = v^2/r + g

0.15 v^2/r = g

v^2 = gr/0.15

v = sqrt(9.81*1.1/0.15) = 8.48 m/sec

Equations are in bold letters.

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