Question

Is it possible to have a negative normal force and if so which direction does the negative force direct the object? If a computer that weighed 25 pounds had a rope tied to it that ran vertically upward over a pulley with a box weighing 50 pounds hanging from the other side would the force that the table exerts on the computer be equal to -25N or is that even possible? Wouldn't the computer accelerate up into the air having a negative force? Or would the object simply have a net force of zero ? Imagining a scenario of the force of a large object on one end of a pulley acting upon an object of a smaller force makes me picture the smaller force getting stuck at the very top of the pulley or eventually being brought down to the table where the box is.

Answer 1

Yes normal force can be negative. The sign of the force is subjective and varies according to the conventions followed by the person, generally we take forces in downward direction as negative and in upward direction as positive which makes a normal force positive. If you reverse the convention used you will have negative normal force which will not affect your calculations if you use the same sign convention during complete solution.

As for the question related to Computer hanging, the answer will be that there will be No force which will be acting from the table on the computer. The extra 25N of force will be from the Tension in the Rope used and not the normal force by table. The table will only apply normal when there will be a force acting on it by the computer, but since the weight of box is greater than the weight of computer hence it will lift the computer and hence no force will be there between computer and table and yes, the computer will accelerate upwards but that will be because of the tension force in the rope and not the normal force due to table.