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TOK physics: Intuition and analogy

Knowledge questions

Is intuition a substitute for knowledge?

Can we understand something without imagining it?

How can analogies aid our understanding?

A lot of physics is about what happened next here is an example:

The image below represents a ship being pulled by two identical tug boats with their engines working at full power. The ropes connecting the  tugs to the boat are kept perpendicular to the ship. What happens to the boat?

Don't reveal the answer below until you have discussed the the possibilities and decided on an answer.

Did you get the right answer?

You probably though that this would happen.

  • What was your argument based on?
  • Did you do an experiment to see what might happen?
  • Did you all agree on the prediction?
  • Did you apply the laws of physics?

Your argument was probably based on intuition and personal experience. If you hold a pencil between two fingers and push the pencil will rotate about the middle point between the fingers. This however isn't the same situation, if you are holding the pencil there are other forces involved such as gravity. If you place the pencil on the table the situation is closer but it is difficult to apply the same force to each side.

Intuition is often not enough to make valid predictions especially when you have no experience of the situation. It is better to apply the laws of physics, in this case Newton's first law.

A body will remain at rest or moving with constant velocity unless acted upon by an unbalanced force.

The tug boats are identical and working at full power so the forces exerted are equal and opposite in other words balanced, this means the centre of mass of the body will not move. The forces are not in the same line so the torques on the ship are not balanced, this causes anticlockwise rotation. Because the centre can't move the rotation takes place about this point.

  • The rotation about the mid point was acheived by adding an axle to act as a pivot. This causes another force. What is the direction of that force at the beginning of the motion?

The centre starts moving up so this extra force must be upwards.

Analogies are very useful in helping us to understand systems that are difficult to imagine, for example the motion of these two pendulums.

The pendulums swing are out of phase but occasionaly they swing in phase. Between 2 times when they are in phase, how many more swings has the faster pendulum made? Try to answer this without counting.

  • Does your answer depend on how fast the faster one swings?

Now consider this analogous situation.

Two runners starting from the same point run around an 400m running track at constant speed. One of the runners is faster than the other and after some time catches up with the slower one. How many more laps has the faster runner completed when they meet?

  • The two questions are the same but, even without an animation, the second is easier to answer, why?
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