• Question: are tall people more likely to fall over than small people if pushed at the same force?

    Asked by efihohall to Adam, Chris, Eleanor, Jessamyn, Sinead on 12 Nov 2013.
    • Photo: Eleanor Holmes

      Eleanor Holmes answered on 12 Nov 2013:


      Good question.

      I am going to imagine that both people are standing up straight with their feet together and their hands by their sides. I will also imagine that both people are in proportion to each other, so the taller person’s legs, arms, torso, etc, are all longer than the shorter person’s by the same percentage. Are you with me?

      Now imagine there is a big red dot right at each person’s belly button. The taller person’s dot is going to be higher above the ground than the shorter person’s. This dot represents the Centre of Gravity. This is the point that we can imagine gravity pulls them towards the Earth from.

      If you push someone over, and they stay completely rigid, they move sideways at an angle and their centre of gravity will no longer be above a stable base (i.e. their legs) and that is how they fall over. Gravity pulls them down. We imagine that their feet are glued to the ground and as such they are falling around a fixed point. The Moment of a rigid body turning about a point is the product of the Mass of the object and the Distance from the turning point to the centre of gravity of the object (This would be so much easier to explain with diagrams).

      So! The taller person is going to have the larger Moment pulling them down and will therefore fall at a smaller angle than the shorter person.

      However! This only works if you set up the experiment exactly as I have said. Of course people don’t fall like pillars all rigid. And there are many different ways you could be standing. If the shorter person raises their arms above their head then they also raise their centre of gravity and they will fall over at a smaller angle than if they keep their arms by their sides. You also have to look at shape. If the short person has very small feet then they will be more unstable. There are too many factors to look at and even in the ideal case I talked about the difference in angle is only about 2 degrees.

      So don’t go around pushing people to investigate this! If you want to do an experiment get some different length cylinders or wooden blocks and find the tipping point as a function of length. It should get bigger the shorter your block.

    • Photo: Adam Murphy

      Adam Murphy answered on 12 Nov 2013:


      Hey, this is the mark of a good question, there’s stuff I want to add to Eleanor’s answer.

      In everyday situations the tall person might do better at not being pushed over.

      In karate and other martial arts you’re told to stand with your feet wide apart. This gives you a good base. If someone pushes against you, your Centre of Gravity shifts to above one foot and you’ll stay standing as long as your centre of gravity is above your base somewhere. So there’s a much bigger space you can stay balanced in.

      Since tall people have longer legs, they can make a much bigger base than a small person and you’d have do to more work to knock them over.

      That said, Eleanor is right too! And this is one of the great things about science, debating different answers and seeing what works where!

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