|3. Everything / Maths, Science & Technology / Physics|
What Happens When You Drop a Slinky
Most of us know the 'Slinky' as a toy. It's a soft spring with flat coils, usually made of metal although plastic ones are sold as well. The Slinky was originally marketed as the 'toy that walks downstairs', and indeed it does just that. It's designed to 'pour' over the standard height of a stair riser, and the trailing end has enough whip as it's pulled from the step above to flip beyond the building stack of coils and fall onto the step two below the one it left. The now-unstable stack above pours down onto its new base, and this gravity-powered cycle repeats again and again. A carefully-positioned Slinky will negotiate a whole flight, turning end over end. It even makes a pleasing sound in the process.
The first time anyone sees a Slinky descend a staircase, surprise and delight are guaranteed. Fewer people, though, have shared the Slinky's other surprising and delightful trick. This Entry looks at what happens when you let go of a free-hanging Slinky (the Slinky Drop) and discusses the physics behind a behaviour that some find counter-intuitive to the point of disbelief.
Basics of the Drop
The Slinky Drop starts by taking hold of the topmost coils of the Slinky across the diameter in one hand, between forefinger and thumb. The coils below are allowed to hang down under their own weight. If an adult stands upright with the Slinky arm stretched out horizontally, the bottom of the spring will clear the floor. (If it doesn't, stand on a chair). Wait for the Slinky to steady, so that there is no significant rise and fall. Then let go.
The interesting aspect of the Slinky Drop is how the lowest point behaves.
If a group of onlookers is asked to anticipate what will happen to the bottom of the Slinky when you let go, the answers are usually diverse. Several possibilities seem plausible, and people with some education in physics often come up with one of two ideas. These are:
The Soft Rod
Although the Slinky is a pliant spring, it's already in equilibrium before you release it. The distance between the two ends therefore stays fixed as it falls, until it hits the floor. Think of progressively stiffer and stiffer springs being dropped. Why should their behaviour materially change with stiffness? You wouldn't expect a broom handle to change length if you dropped it, would you?
The Progressive Collapse
All points on the spring move downwards, because they're all influenced by gravity. The lower coils of the spring experience another force, though, with the spring tension pulling them upwards. There isn't enough force to overcome gravity – if there was, the bottom would still have been rising before you dropped the Slinky, rather than being at rest. There is some force, though, and so the bottom falls slower than the top. The Slinky closes up as it falls, and if the drop height is sufficient it will close up completely before it hits the floor.
At least one of these ideas must be wrong.
The Same Way That Bricks Don't
Try it, and find out what really happens. The bottom of the Slinky does not move at all until all the open coils above have closed up, whereupon the now-collapsed Slinky falls as single mass. For a full second or so before that, the lowest extremity of the Slinky just hovers in space as if by magic.
There is no magic involved, of course.
We know that when we drop a body, we remove a supporting force that balances the weight of the object, so that the body accelerates in a downward trajectory under gravity. In the case of a rigid body, that's all there is to it. Those beguiled by this principle fall into the Soft Rod trap. For a spring, and for non-rigid bodies in general, there are internal forces in play too.
The hanging Slinky is in tension due to its self-weight. Because the weight of the Slinky is distributed, so is the tension. At the top, with the entire weight of the Slinky suspended below, the tension equals the weight. At the bottom there is no underslung weight, and so the tension there is zero.
The bottom of the Slinky is therefore not, as we might have first thought, in equilibrium between a downward force due to its weight and an upward force due to tension. The bottom of the Slinky experiences no forces at all, either before or after the moment of release. Things that experience no force remain in their state of rest or uniform motion, as Newton taught us. In this case, a state of rest applies. There is nothing going on to cause the bottom of the Slinky to move.
If this explanation seems hard to credit, look at the coils of the suspended Slinky before you drop it. At the top, they're stretched apart, but at the bottom the coils are already closed up. There really is no weight acting to stretch them out down there.
Is the Slinky Defying Gravity?
No. Its centre of mass accelerates towards the Earth as normal. To compensate for the stationary bottom, the acceleration at the top is twice that due to gravity. Another way to think about this is to stretch the Slinky out horizontally on a table-top, and let go of both ends at the same time. Now the two ends collapse into the mid-point at equal speeds. It tried to do the same thing in a vertical plane when you dropped it, except with the normal behaviour of a falling object superposed, and with the Slinky's self-weight supplying the force of one hand.
But There's No Such Thing as a Rigid Body!
Correct. All real solid objects exhibit some measure of elastic behaviour, and anything with a finite size exhibits some degree of time-lag behaviour throughout its volume when a local force is applied.
This means that the progressively-stiffer-spring notion presented in the Soft Rod section is another fallacy, and the bottom of the broom handle really does hang in space when you let go of the top, just as the Slinky did. However, the distance travelled by the broom handle top before the bottom wakes up is very small, as is the delay between the top and the bottom starting to move. Both these quantities are too small for us to observe, in fact, but they are not zero.
The Progressive Collapse protagonists were rather close, but got no cigar. Their answer is commonest among engineers, it seems. They reason correctly that the bottom is hardly likely to ascend if it wasn't going up before release, but they then flip into a notion of descending slowly instead, entirely missing the possibility of neutrality. Nature abhors a vacuum, and engineers abhor things that don't move when they're supposed to.
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