Kate is sitting on a 1.5-m-wide porch swing. Because of the rain the night before, the left side of the swing is wet, and Kate sits close to the right side. The mass of the swing seat is 10 kg and Kate's mass is 55 kg. Let the center of mass of Kate be 0.20 m from the right end.

T₂ = 516.1333 N

T₁ = 120.8667 N

Explanation:

Let T₁ = the tension in the left cable

T₂ = the tension in the right cable.

sum of the weights = T₁ + T₂

For Kate,

weight = 55 * 9.8 = 539 N

For swing,

weight = 10 * 9.8 = 98 N

T₁ + T₂ = 637 N

For swing, torque = 98 * 0.75 = 73.5

For Kate, torque = 539 * 1.3 = 700.7

Total clockwise torque = 700.7 + 73.5

= 774.2

For right cable, torque = T₂ * 1.5

T₂ * 1.5 = 774.2

T₂ = 774.2 : 1.5

= 516.1333 N

T₁ = 637 - 516.1333

= 120.8667 N