The County Fair Swing carries the mass of riders and chairs in a circular path i

Question

The County Fair Swing carries the mass of riders and chairs in a circular path in a horizontal plane while suspended by cables or chains. Let's assume that:
Each chair with riders is supported by a single cable
The tension in the cable equals 1.6 x the total weight riders and chair
The speed of the center of mass at the end of the cable is 13 m/s.
Determine the radius of the circular path in meters. The County Fair Swing carries the mass of riders and chairs in a circular path in a horizontal plane while suspended by cables or chains. Let's assume that:
Each chair with riders is supported by a single cable
The tension in the cable equals 1.6 x the total weight riders and chair
The speed of the center of mass at the end of the cable is 13 m/s.
Determine the radius of the circular path in meters. The County Fair Swing carries the mass of riders and chairs in a circular path in a horizontal plane while suspended by cables or chains. Let's assume that:
Each chair with riders is supported by a single cable
The tension in the cable equals 1.6 x the total weight riders and chair
The speed of the center of mass at the end of the cable is 13 m/s.
Determine the radius of the circular path in meters.

Explanation / Answer

if a body is in circular motion the centripetal force acting on it is F = mv^2 /r

given tension = 1.6*mg

now mv^2/r = T ==> r = mv^2/T = mv^2/1.6*m*g = v^2/1.6*g = 13*13/ 1.6*9.8 = 10.778 m

radius of the circular path is 10 .778 m

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