Final answer:
The work done by the tension in an elevator cable as it accelerates upward can be found by calculating the tension using Newton's second law and then multiplying the tension by the distance the elevator travels in the direction of the tension.
Step-by-step explanation:
To calculate the work done by the tension in an elevator cable, we need to know the force applied by the cable and the distance over which this force is applied. Since work is the product of force and displacement in the direction of the force, we can use the formula Work = Force × Distance.
The force exerted by the cable is the tension, which can be calculated by using Newton's second law (F = ma), where m is the mass and a is the acceleration. The tension must overcome both the gravitational force (mg) and provide the additional force needed to accelerate the elevator (ma). Therefore, the tension in the cable is T = mg + ma.
The elevator is given as having a mass of 1700 kg and accelerates upward at 1.5 m/s² over a distance of 15 m. We can calculate the work done using the following steps:
- Calculate the gravitational force: Fg = mg = 1700 kg × 9.8 m/s².
- Calculate the total force needed (tension): T = Fg + ma = 1700 kg × 9.8 m/s² + 1700 kg × 1.5 m/s².
- Calculate the work done by tension: Work = T × displacement = T × 15 m.
With these calculations, you would be able to determine the exact value of work done by the tension.