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I am confused on a certain part of Newton's third law. I know that it states that for every action force there is an equal and opposite reaction force that act of different objects. So, let's say you have an elevator that is suspended by a cable. The elevator's mass is 1kg (I know this is unrealistic but just to make the math easy), so when the elevator is sitting still, the opposing force is -9.8N and the applied force or the tension is 9.8N. There is no net force.

But let's say the elevator's motor suddenly turns on and all of a sudden the elevator and rope( the system) begin to accelerate at 2m/s^2. The net force is 2N (1kg*2m/s^2). In other words, the applied force or the tension in the rope is 3N and the opposing force or the weight is -1N.

Here is my question and although it may sound dumb, please help me understand: when I see this problem the tension in the rope attached to the elevator is 3N. But if the rope is pulling the elevator with three newtons of force, does Newton's third law not say that the elevator must pull down on the rope with 3N of force as the opposite and equal reaction force? If this is the case, why is the rope able to accelerate upward if it is being pulled down with 3N of force.

Another way to look at it is that the motor is pulling with a force of 3N (I think) so the rope must be pulling on the motor with -3N of force. Why can the motor accelerate the rope?

Thank you for all of your help!!

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# Newton's Third Law and Forces in an Elevator

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