Question

For the situation where the ends of a massless rope are attached to two stationary objects (e.g., two trees or two cars) so that the rope makes a straight line, which of the following statements are true?

1) The tension in the rope is the same at all points.
2) The rope will sag in the middle due to gravity.
3) The rope will remain straight if the objects are at the same height.
4) The rope will break if the objects are too far apart.

Answer 1

In a situation where a massless rope is attached to two stationary objects, the tension in the rope is the same at all points. The rope will sag in the middle due to gravity, but it will remain straight if the objects are at the same height. The rope will not break unless the tension exceeds its breaking strength.

Step-by-step explanation:

For the situation where the ends of a massless rope are attached to two stationary objects, such as two trees or two cars, the following statements are true:

1. The tension in the rope is the same at all points. This is because the tension in the rope is determined by the forces applied at the ends of the rope, and according to Newton's third law, the rope pulls with equal force but in opposite directions on the two objects.
2. The rope will sag in the middle due to gravity. This is because the weight of the rope itself causes a downward force, leading to a sagging shape in the middle.
3. The rope will remain straight if the objects are at the same height. If the two objects are at the same height, there will be no net force acting vertically on the rope, and it will remain straight.
4. The rope will not break if the objects are too far apart. The tension in the rope is determined by the forces applied at the ends of the rope, not the distance between the objects. As long as the tension doesn't exceed the breaking strength of the rope, it will not break.