The hangover problem

Many years ago, I was lucky enough to work in “Launch Pad” in the science museum. There were lots of wonderful activities and the following blog posts are about the activities. Launch Pad has been replaced by the equally wonderful “Wonderlab”

https://science-projects.org/wp-content/uploads/2016/10/ch2.pdf

https://www.sciencemuseum.org.uk/home

https://www.sciencemuseum.org.uk/see-and-do/wonderlab-equinor-gallery

The hangover problem

This simple exhibit allowed an investigation into the principle of the counterbalance and can be easily replicated at home with some identical blocks such as dominoes.

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The idea was to get the blocks to reach out as far as possible from the top of a fixed base, which is placed on a table.

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If you simply build out from the base, each block going further out, the whole structure will eventually tilt and fall over, as shown above.

This happens because there is a turning force (caused by gravity) which pulls the blocks down.

The blocks can be made stable by counter-acting the turning force with another in the opposite direction.

So, for example, if you want to build out from a single block, you must counteract the turning force which this will create by placing a block at the back. This will create a turning force in the opposite direction to prevent the whole structure from tilting.

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The exhibit was concerned with counterbalance, turning forces and centre of gravity.

Turning forces

Turning forces, also known as moments, can cause things to turn. They occur when, and only when, there is a force acting at a distance from a point about which an object can turn.

A moment = force (N) x the perpendicular distance between the force and the turning point.

An example of a turning force in action is the use of a spanner to tighten or undo a nut.

In the example below an anti-clockwise turning force is needed to undo the nut

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Something rolling down a slope uses the force of friction. If there were no friction then the object would not roll but slide down the slope.

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Sometimes turning forces act in opposite directions and balance the object.

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In the above example weight is the force and for balance the moment on the left-hand side must equal the moment on the right-hand side.

FLDL = FRDR

You may have experienced something like this in the playground, a seesaw. A heavy person can balance a lighter person by having the heavier person closer to the turning point (also known as the pivot point)

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In the hangover problem, the force was gravity, and it can be thought of as acting through the centre of gravity.

https://www.britannica.com/science/centre-of-gravity

Centre of gravity, in physics, is an imaginary point in a body of matter where, for convenience in certain calculations, the total weight of the body may be thought to be concentrated.

If the arrangement of the blocks was such that its centre of gravity was in front of the turning point (the edge of the fixed base), then the turning force would make the blocks turn and fall, as in the diagram below.

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If the centre of gravity lies behind the turning point, then the block will not be able to turn, because the fixed base will be in the way (this is because the fixed base produces a reaction force to counteract the turning force ….. if the turning point were just a pivot. The arrangement of blocks would only balance at one point).

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If the turning point were just a pivot, the centre of gravity of the blocks would have to be directly above it. Then the turning forces clockwise and the anti-clockwise turning forces would balance.

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However, this would be very unstable, as any slight turning of the blocks would mean there would be a distance between the weight and the turning point.

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So, by arranging the blocks so that the centre of gravity of the arrangement will lie behind the edge of a fixed base, you can ensure that the blocks will be stable. That is why counterbalance was important in the exhibit …. The more you build out from the fixed base, the more you must counteract this, and shift the centre of gravity back behind the fixed base.

Counterbalance

Some of the large cranes you see on building sites use counterbalance, A very heavy counterweight is fixed to the crane’s jib, at the other end from the load being lifted. If this counterweight was not present, there would be a turning force, and the crane would topple over.

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Centre of gravity

When you try to balance, for example, a ruler on your finger (the pivot point), it will only balance if your finger is underneath a point called the centre of gravity. If your finger supports the ruler at any point away from the centre of gravity, the ruler will fall off.

In the case of a normal ruler, the centre of gravity should be exactly hallway along. This is because the turning forces due to the weight to the left are balanced exactly by those on the right. If you were to attach some plasticine to one end of the ruler, the point where the turning forces are balanced will move, as in the diagrams below.

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It is often said that the weight of an object acts ‘through its centre of gravity’. It is often useful to think of it this way. In the hangover problem, the centre of gravity must be behind the edge of the fixed base.

The diagram below shows one possible way of arranging the blocks to give the greatest ‘overhang’. There are other ways, and all of them will involve a counterbalance, and all will have their centre of gravity behind the edge of the fixed base.

The more you build out from the base, the more you must also build back to counteract the turning force which would otherwise tilt the blocks over and make them fall.

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If you try to copy the arrangement in the diagram above, you will need to adjust the blocks very slightly to find the best balance point.

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