An elevator with a mass 1000kg accelerates downward at 3m/s^2. What is the maximum tension the cable can support if it's breaking strength is 15000N? What is the maximum upward acceleration?
I got the maximum tension by doing.
T = (1000kg)(9.8m/s^2)-(1000kg)(3m/s^2) = 6800N
But I cannot get maximum upward acceleration...The answer says it should be 6
To determine the maximum upward acceleration the elevator can have, we need to consider the tension in the cable when it is at its breaking point. Since the elevator is accelerating downward at 3 m/s^2, it means there must be an opposing force in the upward direction to counteract this acceleration. This opposing force is provided by the tension in the cable.
We can start by calculating the maximum tension the cable can support, which you correctly found to be 6800 N. This tension force is the maximum force that can be exerted by the cable without breaking. We can consider this tension force as the maximum upward force acting on the elevator.
To calculate the maximum upward acceleration, we can use Newton's second law of motion, which states: force = mass × acceleration.
In this case, the maximum upward force is 6800 N, and the mass of the elevator is 1000 kg. So, we have:
6800 N = 1000 kg × acceleration
To find the acceleration, we rearrange the equation:
acceleration = 6800 N / 1000 kg
acceleration = 6.8 m/s^2
Therefore, the maximum upward acceleration the elevator can have is 6.8 m/s^2 (approximately).
Note: It seems that there might be a mistake in the answer you mentioned, where the maximum upward acceleration is stated as 6 instead of 6.8. Double-checking the calculations and using the correct value for the maximum tension would yield the correct result.