Final answer:
When you pull horizontally on the free rope attached to the crate, the tension increases in that rope due to the applied force, and as such, the free rope will break first before the one attached to the wall.
Step-by-step explanation:
The question revolves around a scenario where a heavy crate is attached to the wall by a light rope, and another rope hangs from the opposite edge of the crate. You are tasked with determining which rope will break when you pull on the free rope in a horizontal direction, assuming no friction and negligible mass of the ropes. According to Newton's third law, tension in the rope is equal and opposite between the two points of attachment and remains the same throughout the rope. If you pull horizontally on one rope, you create a component of force in the horizontal direction. However, the vertical component of tension due to the weight of the crate still acts on the rope attached to the wall. As the force on the free rope increases, the tension in this rope increases while the tension in the rope attached to the wall is mainly due to the weight of the crate. Therefore, the rope you are pulling on will break first, given that the tension in it exceeds the tension in the rope attached to the wall, which is primarily just supporting the crate's weight.