An elevator with a weight of 27.9 kN is given an upward acceleration of 1.46 m/s2 by a cable.
(a) Calculate the tension in the cable.
(b)What is the tension when the elevator is decelerating at the rate of 1.46 m/s2 but is still moving upward?
To calculate the tension in the cable, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration. In this case, we need to convert the weight of the elevator (27.9 kN) into mass.
(a) Calculate the tension in the cable when the elevator is accelerating upward:
1. Convert the weight from kilonewtons to newtons by multiplying by 1000: 27.9 kN * 1000 = 27,900 N.
2. Calculate the mass of the elevator using the equation: weight = mass * acceleration due to gravity. Rearranging the equation, we have: mass = weight / acceleration due to gravity.
The acceleration due to gravity is approximately 9.8 m/s².
Substituting the values: mass = 27,900 N / 9.8 m/s² = 2,836.73 kg.
3. Now we can calculate the tension in the cable using Newton's second law: Tension = mass * acceleration.
Substituting the values: Tension = 2,836.73 kg * 1.46 m/s² = 4,137.21 N.
Therefore, the tension in the cable when the elevator is accelerating upward is approximately 4,137.21 N.
(b) When the elevator is decelerating at the same rate of 1.46 m/s² while still moving upward, we can use the same calculation as in part (a).
The only difference is that the acceleration will be negative since it's decelerating.
1. Convert the weight from kilonewtons to newtons: 27.9 kN * 1000 = 27,900 N.
2. Calculate the mass of the elevator: mass = 27,900 N / 9.8 m/s² = 2,836.73 kg.
3. Calculate the tension in the cable using Newton's second law: Tension = mass * acceleration.
Since the elevator is decelerating, the acceleration will be negative (-1.46 m/s²).
Substituting the values: Tension = 2,836.73 kg * (-1.46 m/s²) = -4,137.21 N.
Therefore, the tension in the cable when the elevator is decelerating at 1.46 m/s² while still moving upward is approximately -4,137.21 N. The negative sign indicates that the tension is directed downward in this case, acting against the upward motion of the elevator.