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)
Steel Cable 355kg cargo
What is the tension in Condition B?
In Diagram 1.1, the tension in the cable is denoted as FT and the weight of the cargo is denoted as W. To find the tension in the steel cable, we need to consider the forces acting on the cargo.
A. The cargo is stationary:
When the cargo is stationary, the upward tension in the cable must be equal to the weight of the cargo for it to remain at rest. So, FT = W.
Using the equation for weight, W = m * g, where m is the mass of the cargo and g is the acceleration due to gravity (approximately 9.8 m/s^2), we can calculate the weight:
W = (355 kg) * (9.8 m/s^2) = 3481 N
Therefore, the tension in the steel cable when the cargo is stationary is 3481 N.
B. The cargo accelerates upward at a rate of 0.25 m/(s^2):
When the cargo accelerates upward, an additional force is acting on it in the upward direction. This force is equal to the mass of the cargo multiplied by the acceleration.
So, the net force acting on the cargo is the tension in the cable (FT) minus the weight of the cargo (W). Since the cargo is accelerating upward, the net force is given by:
Net force = m * a, where m is the mass of the cargo and a is the acceleration.
FT - W = m * a
Substituting the given values:
FT - 3481 N = (355 kg) * (0.25 m/s^2)
FT - 3481 N = 88.75 N
FT = 3481 N + 88.75 N
FT = 3569.75 N
Therefore, the tension in the steel cable when the cargo accelerates upward at a rate of 0.25 m/(s^2) is approximately 3569.75 N.
To calculate the tension in the steel cable, we need to consider the forces acting on the cargo.
In both conditions, the weight of the cargo always acts downwards, and it is given by the formula:
Weight = mass x gravitational acceleration
= 355 kg x 9.8 m/s^2
Now, let's look at each condition separately:
A. The cargo is stationary:
In this condition, the cargo is not moving, so the tension in the steel cable is equal to the weight of the cargo. Therefore, in Condition A, the tension in the steel cable is:
Tension (A) = Weight
= 355 kg x 9.8 m/s^2
B. The cargo accelerates upward at a rate of 0.25 m/s^2:
In this condition, there is an additional upward force acting on the cargo due to acceleration. Therefore, the total tension in the steel cable will be the sum of the weight of the cargo and the force due to acceleration. The tension in the steel cable is given by:
Tension (B) = Weight + (mass x acceleration)
= 355 kg x 9.8 m/s^2 + (355 kg x 0.25 m/s^2)