A cable lifts a 1060-kg elevator at a constant velocity for a distance of 39 m. What is the work done by each of the following?
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It is needed to answer your question.
To find the work done by each of the following, we can use the equation for work:
Work = Force × Distance × cos(θ)
Where:
- Work is the energy transferred or exerted on an object, measured in joules (J).
- Force is the force applied on the object, measured in newtons (N).
- Distance is the displacement of the object, measured in meters (m).
- θ (theta) is the angle between the force and the displacement vectors.
Since the elevator is lifted at a constant velocity, its acceleration is zero. Therefore, the net force acting on the elevator is zero, and the force applied by the cable must precisely balance the weight of the elevator.
The weight of the elevator can be calculated using the formula:
Weight = mass × gravity
Where:
- Mass is the mass of the elevator, measured in kilograms (kg).
- Gravity is the acceleration due to gravity, which is approximately 9.8 m/s² on Earth.
Let's calculate the work done by each of the following:
1. Work done by the cable lifting the elevator:
Since the elevator is lifted at a constant velocity, the net force acting on it is zero. Therefore, the work done by the cable is also zero.
2. Work done by the gravitational force on the elevator:
The gravitational force is acting in the downward direction, opposite to the displacement of the elevator. Therefore, the angle θ between the force and displacement vectors is 180 degrees. Hence, we can calculate the work done by the gravitational force as:
Work = Force × Distance × cos(θ)
Plugging in the values:
Work = (Weight of the elevator) × (Distance) × cos(180°)
The weight of the elevator can be calculated using the formula mentioned earlier:
Weight = mass × gravity
Plugging in the values:
Weight = (1060 kg) × (9.8 m/s²)
Once we have the weight, we can determine the work done:
Work = (Weight) × (Distance) × cos(180°)
Finally, we can calculate the numerical value of the work done by the gravitational force.