Question

Two wires are tied to a sphere of 1 kg of mass. The sphere is rotated in a horizontal circle at a constant speed of 3.0 m / s. Determine the tensions in each wire.

Answer 1

here,

The two wires and the mast make an equilateral triangle 120 degree- 30 degree - 30 degree,

so we know the bottom wire has a length of 1 m.

The bottom wire is the hypotenuse of a right triangle 30degree- 60 degree - 90 degree with the mast and the radius of spin as the other two sides.

This means the radius r = sqrt(3) / 2 m

The tension is the same in the two wires, so summing forces in the vertical direction to zero

Tcos(60) + T cos(30) - 1(9.8) = 0

T = 7.18 N

the tension in each wire is 7.18 N