An empty elevator of mass 2.7x10^2kg is pulled upward by a cable at an acceleration of 1.2m/s. What is the tension in the cable? What would the tension be if the elevator were accelerating downward at 1.2m/s^2?
Tension= mg+ma where a is the accelearation upward (downward will be negative)
To find the tension in the cable, we can use Newton's second law of motion, which states that the force acting on an object is equal to its mass multiplied by its acceleration.
In the first scenario, where the elevator is being pulled upward with an acceleration of 1.2 m/s², the tension in the cable is given by the equation:
Tension = Mass * Acceleration
Tension = (2.7 × 10² kg) * (1.2 m/s²)
Tension = 324 kg·m/s²
Therefore, the tension in the cable when the elevator is accelerating upward is 324 kg·m/s².
In the second scenario, where the elevator is accelerating downward at 1.2 m/s², we need to account for the opposite direction of acceleration. In this case, the tension in the cable will be:
Tension = Mass * (Acceleration + g)
Here, g represents the acceleration due to gravity, which is approximately 9.8 m/s² (assuming the elevator is on Earth). Plugging in the values:
Tension = (2.7 × 10² kg) * (-1.2 m/s² + 9.8 m/s²)
Tension = (2.7 × 10² kg) * (8.6 m/s²)
Tension = 2772 kg·m/s²
Therefore, the tension in the cable when the elevator is accelerating downward is 2772 kg·m/s².