Question

Reviewing Interactive Solution 5.46 will help in solving this problem. A stone is tied to a string (length = 0.551 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 9.60% larger than the tension that exists when the circle is horizontal. Determine the speed of the stone.

Answer 1

The speed of the stone is

v = 7.45 m/s

Step-by-step explanation:

Length, L=0.551m

maximum tension in the spring = 9.6%

So let speed of stone be

Tv = TH + 9.6/ 100 * TH

Tv - m*g = m*v^2/L

TH = m*v^2 / L

Factor mass to cancel in the equation

Solve to v

v^2= L*g*100 / 9.6

Replacing numeric:

v^2=0.551m*9.8m/s^2*100 / 9.6

v = sqrt( 56.24 m^2/s^2)

v = 7.45 m/s