Solve Work Problems: Elevator with Mass 1000kg on Single Cable

[johnj7]

Hello, I'm currently studying for the mcat and ran across this problem in one of my practice tests.

An elevator used in a building has a mass of 1000 kg when empty
the elevator hangs on a single cable

step 1. the elevator rises for 2m/s^2 for 3 seconds,
if there is no friction on the elevator or cable, what is the work done on the elevator?

the correct answer is 108 kJ

I understand how to get the answer
T - mg = ma
T = ma + mg = 12000

W = Fd = 12000 X 9 m = 108 kJ

but why in this case do we only use the force in the Tension, I thought we always use NET force, or in this case Fnet = T - mg = 1000 X 2 = 2000
w = fd = 2000 X 9 = 18 kJ

so why just tension and not Net force?

thank you!

 

[PhanthomJay]

You are quite right, the net or total work done on the elevator is 18 kJ; the work done by the cable is 108 kJ and the work done by gravity is -90 kJ. I guess the problem was not properly worded.

 

[nlightner]

I can explain why we only use the tension force in this problem and not the net force. In this scenario, the elevator is moving in a straight line, which means that the net force acting on it is zero. This is because the elevator is not accelerating in the horizontal direction, so the sum of all horizontal forces must be zero according to Newton's First Law of Motion. Therefore, the only force that is doing work on the elevator is the tension force, as it is the only force acting in the direction of motion.

Furthermore, the net force is not always used in work problems. Work is defined as the product of the force applied and the distance moved in the direction of the force. In this case, the tension force is the only force that is causing the elevator to move and therefore it is the only force that is doing work. The net force may be used in other types of problems, such as calculating the acceleration of an object, but it is not necessary for solving work problems.

I hope this explanation helps clarify why we only use the tension force in this elevator problem. Keep up the good work with your MCAT studies!