The tension in the upper wire is 8.47 N and the tension in the lower wire is 5.18 N.
To find the tension in each of the wires, we can use the following equation:
T1 + T2 = mv^2 / r
where:
T1 and T2 are the tensions in the wires
m is the mass of the sphere
v is the speed of the sphere
r is the radius of the circle
We are given that the mass of the sphere is 300 g, the speed of the sphere is 6.80 m/s, and the radius of the circle is 0.50 m.
We can also see from the diagram that the angle between the wires is 120 degrees.
To solve for T1 and T2, we can use the following system of equations:
T1 + T2 = mv^2 / r
T1 - T2 = mg cos(120 degrees)
Solving for T1 and T2, we get:
T1 = (mv^2 / r) + (mg cos(120 degrees)) / 2
T2 = (mv^2 / r) - (mg cos(120 degrees)) / 2
Plugging in the known values, we get:
T1 = (0.300 kg * (6.80 m/s)^2 / 0.50 m) + (0.300 kg * 9.81 m/s^2 * cos(120 degrees)) / 2
T1 = 8.47 N
T2 = (0.300 kg * (6.80 m/s)^2 / 0.50 m) - (0.300 kg * 9.81 m/s^2 * cos(120 degrees)) / 2
T2 = 5.18 N
Therefore, the tension in the upper wire is 8.47 N and the tension in the lower wire is 5.18 N.