1J30.35 Rope and Two Students

A long rope is suspended between a fixed object and a strong student. Pulling along the rope, a weaker student will find it difficult to displace the stronger student. Pulling perpendicular to the rope, the weaker student easily wins the tug of war. Alternatively, this demo can be done by having two stronger students pull on the ends of the rope, instead of one stronger student pulling on one end with the other end attached to the wall. Then it looks like a single student single-handedly overpowers two others by the sheer power of physics.

This slightly blurred photo shows a large lecture space. At the far end, a student pulls with determination on the end of a rope. The other end of the rope is out of the frame, but judging by appearances, is probably held in the sturdy grip of another student. In the middle of this tug-of-war, a third student lays a single hand on the middle of the rope and exerts a perpendicular force, so that the rope makes an obvious angle out to the middle student and back to the first student.

For small angles, 1/sin(θ) is large and for a small force F the tension required of the stronger student to resist being dragged is large. For example, at θ = 10˚, 1/sin(θ) = 5.8 and T ≈ 3F to be stable. The student pulling at the end of the rope would have to be three times as strong as the other student to avoid getting pulled when θ = 10˚.

This sketch shows a rope attached to a wall at the left. At the far right, the rope is held by a student. In the middle, another student is depicted pulling back on the rope. The tension is shown pointing toward the student pulling at the end of the rope (right). A force F is shown pointing back toward the middle student (left). We also see the equation F is less than or equal to T.In this sketch, a rope is attached to a wall at the left. The rope extends out to end at the right-hand side (student not depicted). A dashed line shows the straight-line path of the rope if it were simply under tension at the right end. However, a force pulls the rope upward at the center of the rope, such that the rope forms a triangle with the straight-line path as the hypotenuse. At the center of the rope, an upward force F is shown. At each end, the angle theta is defined between the straight-line path and the actual path of the rope. Two tensions T are drawn, each originating at the center point of the rope. One points along the rope to the left, the other along the rope to the right. Below the sketch is the equation F is equal to 2 times T times sin theta. Below that, the equation is solved as T is equal to F divided by 2 sin theta.

 

Locations: Manila Rope D2-6