find the tension in each cable.
T1=68.0 degree
T2= 25.0 degree
weight= 27500 N
To find the tension in each cable, we can use the concept of equilibrium. At equilibrium, the sum of the forces acting on an object must be zero.
Let's assume there are two cables, cable 1 and cable 2, both exerting tension on an object. The angles formed by the cables with the vertical direction are T1 (68.0 degrees) and T2 (25.0 degrees), respectively.
First, let's resolve the weight (27500 N) into its vertical component (mg*cosθ) and horizontal component (mg*sinθ).
Vertical component = 27500 N * cos(90°) = 0 N (since cos(90°) = 0)
Horizontal component = 27500 N * sin(90°) = 27500 N
Now, let's consider the vertical forces acting on the object:
T1 * cos(T1) - T2 * cos(T2) = 0 (since the vertical components of tension must add up to balance the weight)
Next, let's consider the horizontal forces:
T1 * sin(T1) + T2 * sin(T2) = 27500 N (since the horizontal components of tension must balance the horizontal component of the weight)
We can solve these two equations to find the values of T1 and T2.
Now, let's calculate the values using these equations.
For the vertical forces equation:
T1 * cos(68.0°) - T2 * cos(25.0°) = 0
For the horizontal forces equation:
T1 * sin(68.0°) + T2 * sin(25.0°) = 27500 N
By rearranging and solving these equations, you can find the tension in each cable.
Note: Please make sure to use the appropriate units (e.g., radians or degrees) when evaluating trigonometric functions on your calculator.