How much silly putty would cover the Earth?

26 July 2015

Question

We have a tin of Silly Putty and it is slowly enveloping a can of 35p energy drink. It is a 3oz blob and we were wondering how much of this we would need the putty to envelop the globe?

Answer

We put this question to Ewen Keller.

Ewen - I really think this is one of these crazy questions that you can treat a number of different ways. Chris - Not with a pinch of salt though because that would stop the silly putty working. Ewen - Yeah, that's very true. But I thought I'd just give it a go and do some simple calculations in relation to sort of how much area is in the earth or around the earth, which a simple bit of maths, 4πr2 [four pi r squared] gives you the area which works roughly out to be 510 million square kilometres. Chris - That's the surface area of our whole planet. Ewen - Yeah. Though again, I kind of wonder from the source I looked up whether that actually includes all the humps and bumps, and going up to the Himalaya or not, which will obviously increase the area a bit more. But if we assume for simplicity's sake, it's 510 million square kilometres. The next question then is, how much silly putty do we want to cover the earth? Just for simplicity's sake, I decided to make it 1 centimetre deep. Basically, if you do the number crunching as far as I could get, you end up with needing a large piece of silly putty that's going to be 5.1 trillion tons in weight. So, that's 5.1 thousand billion tons in weight to use the terminology that we have for money matters that we hear so much about in the news. Chris - Does it float? Ewen - Well, I was going on the basis that it would have the same density as water. So, I decided to go for 1 gram per cubic centimetre again, for simplicity. Now, that amount of silly putty, if you were to actually make it into a cube would actually be a cube side of 17 kilometres in size. So, we're talking a pretty big lump of silly putty. Chris - Assuming you started at the top and plonked it on the north pole, and then let it sort of smear itself out, there would be a thermal effect as well because would the low temperature affect the material behaviour? Ewen - It probably would. It would slow it down quite a lot. Chris - What could we do to compensate? Would we have to heat it up? Ewen - Yeah. It is often quite a dark colour anyway. So, if it covers the north pole, then it will give you some increased global warming. So, that would probably speed things up a bit.

Chris - So it might be a self-fulfilling prophecy. It may speed things up and help it smear out more. Why does it have those weird properties? What's special about the material that is silly putty that makes it do that? Ewen - Basically, it's the way in which it links together at a molecular level. Basically, it's called a non-Newtonian fluid. So, it doesn't obey the laws of Newtonian physics. As a result of that, it has one or two peculiar properties that if you let it sit on its own, it will actually flow like you would imagine a normal liquid to be. But if you subject it to a rapid force, and this is because the molecules are sort of locked in a way that makes them resist force in a temporary manner. So, if you hit a piece of silly putty with a hammer for example, it will actually act as if it's a solid and you can actually break a bowl of silly putty up by almost fracturing it. And then if you let it sit for a while, it will then go back into blobs. So, it's a little bit like the guy in Terminator 2 when he gets frozen solid and basically, he got hit and got smashed into lots pieces but then became a liquid and became whole again. so, silly putty is a very interesting class of materials. Corn flour in water does exactly the same thing. Anyone who's been to the science festival in Cambridge will have enjoyed running over pots of corn flour, but you don't want to hang around for too long. Otherwise, you sink into it up to your knees.

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