A cable lifts a 1200 kg elevator at a constant velocity for a distance of 34.5 m. What is the work done by the tension in the cable.
M g H
g is the acceleration of gravity
M and H are mass and height increase
To find the work done by the tension in the cable, we can use the formula:
Work = Force × Distance × cos(θ)
where:
- Force is the tension in the cable
- Distance is the distance the elevator is lifted
- θ is the angle between the force and the direction of motion (in this case, since the elevator is lifted vertically, θ = 0° and the cosine of 0° is 1, so we can omit this from the equation)
First, let's calculate the force. The weight (force due to gravity) experienced by the elevator can be calculated using the formula:
Weight = mass × acceleration due to gravity
where:
- Mass is the mass of the elevator (1200 kg)
- Acceleration due to gravity is approximately 9.8 m/s^2
Weight = 1200 kg × 9.8 m/s^2 = 11,760 N
Since the elevator is being lifted at a constant velocity, the upward force (tension in the cable) must be equal to the weight of the elevator.
Therefore, the force exerted by the tension in the cable is 11,760 N.
Now, we can calculate the work done by the tension.
Work = Force × Distance
Work = 11,760 N × 34.5 m
Using the equation:
Work = 11,760 N × 34.5 m = 405,720 Joules
So, the work done by the tension in the cable is 405,720 Joules.
To find the work done by the tension in the cable, we can use the formula:
Work = Force × Distance × cos(θ)
Where:
- Work is the amount of energy transferred or done
- Force is the force applied to move an object
- Distance is the distance over which the object is moved
- θ is the angle between the force and the direction of displacement
In this case, the force applied to lift the elevator is the tension in the cable. Since the elevator is lifted at a constant velocity, we know that the net force acting on the elevator is zero. Therefore, the tension force in the cable must be equal to the force of gravity pulling the elevator downward.
The force of gravity on the elevator can be calculated using the formula:
Force of gravity = mass × gravitational acceleration
The mass of the elevator is given as 1200 kg, and the gravitational acceleration is approximately 9.8 m/s^2.
Force of gravity = 1200 kg × 9.8 m/s^2 = 11,760 N
Now let's calculate the work done by the tension in the cable using the given distance of 34.5 m.
Work = 11,760 N × 34.5 m × cos(180°)
The angle between the force of gravity and the direction of displacement is 180° because the cable pulls vertically upwards while the displacement is vertical as well.
cos(180°) = -1
Work = 11,760 N × 34.5 m × (-1) = -405,720 J
Therefore, the work done by the tension in the cable is -405,720 Joules. The negative sign indicates that the work done by the tension is in the opposite direction of the displacement, which means the tension force is doing negative work.