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.
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?
1 answer
1 answer