Final answer:
To find the tension forces on the two strings, you need to break down the given angles into their respective components. Use the weight of the object and the horizontal and vertical components of the tension forces to set up a system of equations. Solve these equations simultaneously to find the tension forces on the two strings.
Step-by-step explanation:
To find the tension forces on the two strings, we need to break down the given angles into their respective components. Let's call the tension force on the left string T₁ and the tension force on the right string T₂. Since the left string hangs at a 35° angle, the vertical component of T₁ is T₁ * sin(35°) and the horizontal component is T₁ * cos(35°). Similarly, for the right string, the vertical component of T₂ is T₂ * sin(50°) and the horizontal component is T₂ * cos(50°).
Now, we can set up a system of equations using the given conditions. Since the object is in equilibrium, the vertical component of the tension forces must equal the weight of the object (64N). So, we have T₁ * sin(35°) + T₂ * sin(50°) = 64N. The horizontal components of the tension forces must cancel each other out, so we have T₁ * cos(35°) = T₂ * cos(50°).
We can now solve these equations simultaneously to find T₁ and T₂. Substitute T₂ * cos(50°) for T₁ * cos(35°) in the first equation to get T₁ * sin(35°) + (T₂ * cos(50°)) * sin(50°) = 64N. Rearrange this equation to solve for T₂:
T₂ = (64N - T₁ * sin(35°)) / (cos(50°) * sin(50°)).
Next, substitute this value of T₂ into the second equation to solve for T₁:
T₁ * cos(35°) = ((64N - T₁ * sin(35°)) / (cos(50°) * sin(50°))) * cos(50°).
Simplify and solve for T₁ to find the tension force on the left string. Substitute this value back into the first equation to find the tension force on the right string.