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)
What is the tension in Condition A?
.
In Condition A, when the cargo is stationary, there is no acceleration. Therefore, the net force on the cargo is zero.
The weight of the cargo, W, is acting downward, and the tension, FT, in the steel cable is acting upward. To have a net force of zero, the tension must be equal in magnitude to the weight. Therefore, the tension in Condition A is equal to the weight of the cargo.
Tension in Condition A = Weight (W)
In Condition A, where the cargo is stationary, the tension in the steel cable can be calculated as follows:
1. Identify the forces acting on the cargo in the diagram, which are the weight (W) and the tension in the cable (FT).
2. Since the cargo is stationary, it means that the net force acting on it is zero. This means that the tension in the cable (FT) must be equal in magnitude but opposite in direction to the weight (W).
3. Use Newton's second law, which states that the net force on an object is equal to the mass of the object multiplied by its acceleration:
Fnet = m * a
4. In this case, since the cargo is stationary, its acceleration (a) is zero. Therefore, the net force (Fnet) is also zero.
5. Since the net force is zero, the tension in the cable (FT) must be equal in magnitude but opposite in direction to the weight (W).
FT = -W
Note: The negative sign indicates that the direction of the tension is opposite to the weight.
Therefore, in Condition A, the tension in the steel cable is equal in magnitude but opposite in direction to the weight.
Let's say the weight (W) is 1000 N. Then, the tension in the cable (FT) would be:
FT = -W
FT = -1000 N
So, the tension in Condition A is -1000 N.