In a shipping yard, a crane operator attaches a cable to a 1130-kg shipping container and then uses the crane to lift the container vertically at a constant velocity for a distance of 30 m. Determine the amount of work done by each of the following.
(a) the tension in the cable
J
(b) the force of gravity
J
(a)w=mgh=1130*9.8*30
(a) the tension in the cable: Well, the tension in the cable is doing the lifting, so it's doing the work. And since the container is being lifted at a constant velocity, there is no change in kinetic energy. Therefore, the work done by the tension in the cable is zero joules.
(b) the force of gravity: Ah, gravity! Always pulling things down. Since the container is being lifted vertically, the force of gravity is working against the motion. However, the container remains at a constant velocity, so there is no net change in kinetic energy. This means that the work done by the force of gravity is also zero joules.
So, to summarize:
(a) the tension in the cable: 0 J
(b) the force of gravity: 0 J
Well, that's not very exciting, is it? But hey, at least no work means no worry!
To determine the amount of work done by each of the following, we can use the formula for work:
Work = Force x Distance x Cosine(angle)
In this case, since the container is being lifted vertically, the angle between the force and the distance is 0°, and thus the cosine of 0° is 1. Therefore, the formula simplifies to:
Work = Force x Distance
(a) To determine the work done by the tension in the cable, we need to find the force exerted by the tension. This force is equal to the weight of the container, which can be calculated using the formula:
Weight = mass x acceleration due to gravity
Given that the mass of the container is 1130 kg, and the acceleration due to gravity is approximately 9.8 m/s^2, we can calculate:
Weight = 1130 kg x 9.8 m/s^2 = 11074 N
Now, we can calculate the work:
Work = Force x Distance = Weight x Distance = 11074 N x 30 m = 332,220 J
Therefore, the amount of work done by the tension in the cable is 332,220 J.
(b) To determine the work done by the force of gravity, we can use the same formula:
Work = Force x Distance
In this case, the force of gravity is acting in the opposite direction of the displacement, since the container is being lifted vertically. Therefore, the work done by the force of gravity is negative.
Work = -Force x Distance = -Weight x Distance = -11074 N x 30 m = -332,220 J
Therefore, the amount of work done by the force of gravity is -332,220 J.
To determine the amount of work done by each force, we need to use the formula for work:
Work = Force * Distance * cos(theta)
where:
- Force is the magnitude of the force applied
- Distance is the distance over which the force is applied
- theta is the angle between the force and the direction of motion
(a) Tension in the cable:
Since the container is lifted vertically at a constant velocity, the tension in the cable must be equal to the force of gravity acting on the container.
To find the tension in the cable, we can use Newton's second law, which states that the net force acting on an object is equal to its mass multiplied by its acceleration:
Force = mass * acceleration
In this case, the acceleration is zero since the container is lifted at a constant velocity, so the net force is also zero. Therefore, the tension in the cable is equal to the force of gravity.
Force of gravity = mass * acceleration due to gravity
F_gravity = 1130 kg * 9.8 m/s^2
Now, we can calculate the work done by the tension in the cable:
Work_Tension = Force_Tension * Distance * cos(theta)
Since the tension in the cable and the distance are both vertical, the angle (theta) between them is 0 degrees. The cosine of 0 degrees is 1, so:
Work_Tension = F_gravity * Distance * cos(0)
Work_Tension = (1130 kg * 9.8 m/s^2) * 30 m * 1
Work_Tension = 332,400 J
Therefore, the amount of work done by the tension in the cable is 332,400 Joules (J).
(b) Force of gravity:
The force of gravity is the weight of the container, which can be calculated using the formula:
Force_gravity = mass * acceleration_due_to_gravity
Force_gravity = 1130 kg * 9.8 m/s^2
Now, we can calculate the work done by the force of gravity:
Work_gravity = Force_gravity * Distance * cos(theta)
Since the distance and the force of gravity are both vertical, the angle (theta) between them is 0 degrees. The cosine of 0 degrees is 1, so:
Work_gravity = Force_gravity * Distance * cos(0)
Work_gravity = (1130 kg * 9.8 m/s^2) * 30 m * 1
Work_gravity = 332,400 J
Therefore, the amount of work done by the force of gravity is 332,400 Joules (J).