Final answer:
The tension developed in cable AB is 7.5 kN, the tension developed in cable AC is 7.5 kN, and the tension developed in cable AD is 0 kN.
Step-by-step explanation:
To determine the tension developed in cables AB, AC, and AD, we can analyze the forces acting on the tractor tread assembly. Since the assembly is lifted at a constant velocity, we know that the net force acting on it is zero.
Let's consider the forces acting on the assembly:
- The force applied at point A, which is 15 kN upward.
- The tension in cable AB, which pulls the assembly to the left.
- The tension in cable AC, which pulls the assembly upward and to the right.
- The tension in cable AD, which pulls the assembly downward and to the right.
Since the assembly is in equilibrium, the sum of the forces in the horizontal direction and the sum of the forces in the vertical direction must be zero.
In the horizontal direction:
Sum of horizontal forces = Tension in AB - Tension in AC + Tension in AD = 0
In the vertical direction:
Sum of vertical forces = Tension in AC + Tension in AD - 15 kN = 0
From these two equations, we can solve for the tensions in the cables:
Tension in AB = Tension in AC - Tension in AD
Tension in AC + Tension in AD = 15 kN
Substituting the second equation into the first equation, we get:
Tension in AB = 15 kN - Tension in AC
Now, we can substitute this expression for Tension in AB into the second equation:
Tension in AC + Tension in AD = 15 kN
Tension in AC + (15 kN - Tension in AC) = 15 kN
Simplifying this equation, we find:
2 * Tension in AC = 15 kN
Tension in AC = 7.5 kN
Substituting this value back into the equation for Tension in AB, we get:
Tension in AB = 15 kN - 7.5 kN = 7.5 kN
Finally, the tension in cable AD can be found by substituting the values of Tension in AC and Tension in AB into the equation:
Tension in AD = 15 kN - Tension in AC - Tension in AB
Tension in AD = 15 kN - 7.5 kN - 7.5 kN = 0 kN