A man pulls on a (massless) rope tied to a tree with a force of 500 N. Later, two men pull on opposite ends of the same rope with opposing forces of 500 N each. The tension in the rope is .

Explanation:

It may be that in the case of the tree, the result is more intuitive, because you can think that there is only one force. But this is misleading.

To find the tension in the rope, you should draw a free body diagram. By doing so, you would find that the rope is static because there are two opposite forces. Assuming, for simplicity, that the rope is horizontal,  a force of 500N is pulling to one direction (let's say to the right) and a force of 500N is pulling to the opposite direction (to the left). Else, the rope would not be static.

That analysys is the same for the rope tied to the tree ( the tree is pulling with 500N, such as the man, but in opposite direction) and when the rope is pulled  by two men on opposite ends, each with forces of 500N.

Hence, the tension is the same and equal to 500N.