Will it fall?

Identifying and differentiating weight, tension, friction, and centrifugal forces.

Understanding what causes the strong friction of a string or rope wound around a cylinder.

Hand out strings with a length of about 1 meter, and let the students choose the weights they want to attach. Make sure that students only use objects without sharp edges (e.g. an eraser) - when the smaller weight swings around the pencil, it could hit someone.

Attach weights on both ends of the string, one weight being about 10 times heavier than the other. Then drape the string over the pencil, with the heavier weight hanging a few centimeters under the pencil. With the other hand, hold the small weight at the height of the pencil, so that the string is stretched horizontally before you. Then let go of the smaller weight.

1.Why does the small weight wrap around the pencil?

2. How does the small weight hold the much heavier weight, once it is warped 4 or 5 times around the pencil?

How would the small weight behave, if the heavier weight was not falling?
› If the heavier weight is hold in place, the smaller weight just swings as a pendulum.

What happens to the smaller weight while it is drawn to the pencil?
› It rotates faster around the pencil.

Why is the friction of the string hanging over the book so much smaller than the friction of the string wound around the pencil?
› The force pressing the string onto the book – and thus the force causing frictions – is only the tiny weight of the string, not the weight of the objects attached to it. This is because the force that these weights cause, namely the tension in the string, is directed parallel to the book surface. Wound around the pencil, however, a part of the tension in the string presses the string against the pencil, leading to the large friction force.

While the small weight swings around the pencil like a pendulum, this pendulum's length quickly gets shorter as the falling heavier weight draws on the string. Due to the conservation of angular momentum, the rotation of the small weight around the pencil increases as its radius decreases. The small weight thus spirals inward around the pencil and the centrifugal force slows down the fall of the heavier object.

However, this effect is small compared to the friction between the pencil and the string that winds around it. This friction force increases exponentially with the number of turns around the pencil - but not because of the change in surface where string and pencil touch. If that was the case, the string draped over the book should experience the same large friction and stop the fall of a heavier object. Interestingly enough, the radius of the pencil has no influence either - the strength of the friction only depends on the friction coefficient and the angle at which the string is wound around the pencil: As the tension force in the string changes direction, a part of it presses the string against the pencil, causing the large friction. Because of this so-called belt friction, the tension on the two ends of the string can differ significantly, and a small weight can 'hold' a much heavier object from falling further.