SILLY PUTTY

1943 was a good year. The Slinky was invented that year, the author was born that year and Silly Putty was also invented that year.

Silly Putty is not just a toy that made it to the National Toy Hall of Fame. Variations of silly putty (see www.d3o.com) are now being used as shock absorbing materials for sports wear and footwear. The essential physics is that silly putty is elastic on a short time scale and viscous on a long time scale. It will bounce when you drop it since the impact time is very short. But it will stretch when you pull it since the force is applied for a long time. Long enough to untangle some of the long chain molecules in the polymer and long enough to break weak hydrogen bonds that link the long molecules. Like other polymers, the long molecules are not laid out in straight lines but become entangled during manufacture, like long strands of spaghetti.

Silly putty is described as being viscoelastic, as are thousands of other materials such as nylon, rubber, wood, food, human tissue, baseballs, tennis strings, earth, lava, etc. Almost any solid that is not a metal is viscoelastic to some extent. Understanding silly putty provides useful clues as to how all those other materials behave.

Here are two short movie clips, filmed at 300 frames/sec, showing how light balls and heavy balls bounce when they are dropped on a cylinder of silly putty. You can see what is happening more clearly when the heavy ball is dropped. The light steel ball (28 grams) bounces off quickly, in about 0.004 sec, before any of the molecules have had time to be untangled. Silly putty is definitely elastic on that short time scale.

The heavy steel ball (2.0 kg) also bounces, but not as well. The impact takes 0.04 seconds in this case, and during that time the putty starts flowing like a viscous fluid. It never fully recovers from the blow and suffers “permanent” deformation. Restitution is not complete, so the collision is one with a low coefficient of restitution. Of course, silly putty can be rolled up into another cylinder and squashed endlessly just for fun. That’s because the weak hydrogen bonds and untangled molecules can be reassembled on a long time scale, provided a force is applied to allow the putty to flow back to where it was before it was squashed.

The behaviour of silly putty can be modelled using a spring and a dashpot in series to simulate its elastic and viscous properties. For a spring, F = kx where k is the spring constant. For a dashpot, F = C dx/dt where C is a constant proportional to the viscosity and dx/dt is the speed at which the dashpot or the silly putty is squashed or stretched. The ratio C/k measures the relaxation time, which is a measure of the time taken for the material to flow. The relaxation time is about 0.1 second for silly putty, so it starts flowing easily almost as soon as you start to stretch or squash it. When a large force is applied during a collision with silly putty, the relaxation time decreases to about 0.025 sec, which is why the 2 kg ball bounce was not as elastic as the 28 gram ball bounce.

Baseballs and other sports balls also flow when they are squashed, but they are generally much stiffer and much more viscous so the visual effects are much less obvious. Most sports balls don’t bounce very well. That’s because they are viscous and lose some of their elastic energy when they bounce.

If silly putty is squashed by say 10 mm and then it remains squashed by that amount, then the force on the putty drops rapidly with time due to “stress relaxation”. If a metal spring is squashed by 10 mm then it needs a force to hold it in that squashed position. If the force is removed, the springs returns to its original length. If silly putty is squashed by 10 mm and held like that for a second or two then it doesn’t spring back when the force is removed. But if the force is applied for less than 0.1 sec, then it will spring back to some fraction of its original length depending on the time the putty remains compressed. That is why silly putty behaves like a spring in series with a dashpot. It has both elastic and viscous properties.

For more information, see:

R. Cross, Elastic and viscous properties of silly putty, Am. J. Phys. 80, 870-875 (2012).

R. Cross, Elastic properties of plasticine, silly putty and tennis strings, The Physics Teacher, 50, 527- 529 (2012).