Given DIAGRAM 1.1 where FT means Tension and W means Weight, calculate the tension on the steel cable given the following conditions:
A. The cargo is stationary.
B. The cargo accelerates upward at a rate of 0.25 m/(s^2)
Without the DIAGRAM 1.1, it is not possible to accurately determine the tension on the steel cable. Please provide the necessary information and the diagram for a more precise answer.
To calculate the tension on the steel cable in both scenarios, we need to consider the forces acting on the cargo. In both cases, the weight of the cargo will act downward, and the tension in the cable will act upward.
A. The cargo is stationary:
In this case, since the cargo is not accelerating, the net force acting on it is zero. Therefore, the tension in the cable must be equal to the weight of the cargo.
Tension (FT) = Weight (W)
B. The cargo accelerates upward at a rate of 0.25 m/(s^2):
To calculate the tension in the cable when the cargo is accelerating, we need to consider the net force acting on the object.
The net force is equal to the mass of the cargo multiplied by its acceleration. This net force must be equal to the sum of the tension and weight forces:
Net force = Tension + Weight
Now, the weight of an object can be calculated using the formula: Weight = mass x acceleration due to gravity (g).
Given that the acceleration due to gravity is approximately 9.8 m/s^2, we can calculate the weight:
Weight = mass x g
Since we know the acceleration of the cargo (0.25 m/s^2) and the acceleration due to gravity, we can calculate the net force:
Net force = mass x (acceleration + g)
Now, we can substitute the net force back into the equation:
Net force = Tension + Weight
Solving for the tension:
Tension = Net force - Weight
Therefore, to calculate the tension on the cable when the cargo accelerates upward at a rate of 0.25 m/(s^2), we need to calculate the net force and weight, and then subtract the weight from the net force.