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I saw a statement in my HC Verma's physics book.

One should take smaller steps while walking on ice since it ensures smaller friction force.

Now let us say there is a man M of mass 50kg standing on ice and the maximum distance he could cover in a single step without slipping is 15cm.

Now an observer A (who is at rest) observes that the man moves $10\;cm$in $1 \;sec$ in a single step. So for him he doesn't slip and simply manages to move $10\;cm$.

If the same person is observed from a frame B moving with $10\;cm/s$ in the opposite direction of what M's motion is according to A then for B, the man M moves $20\;cm$ in $1 \;sec$ and this distance is also covered again in a single step (which is quite obvious) but this means that for B the man M should seem to fall down but this will break the symmetry between the two inertial frames .

So what's wrong with this experiment ? Can't we use this technique to distinguish between two inertial frames ? Why/ why not ?

Ankit
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  • The step size one should do to avoid slipping on ice is not an imperative, it's merely advice on prundent behavior. Even if the person takes large step, they may or may not slip. There is no cause-and-effect relationship being tested. – Bill N Feb 07 '21 at 16:44
  • @Bill N don't we need to push hard to take a large step ? – Ankit Feb 07 '21 at 17:12

2 Answers2

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The point is that the ice is moving in one frame and not in the other. Classically, the speed of the man relative to the ice is the same in any inertial frame.

Ankit
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Ben51
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  • so in the moving frame the man moves 10cm on the ice and the ice itself moves 10cm . Right ? – Ankit Feb 07 '21 at 17:49
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    @Astudent Sure. And since the step size thing is based on static friction between feet and ice, it’s the speed/step size relative to the ice that matters. – Ben51 Feb 07 '21 at 17:51
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Someone flying by the Earth in a rocket with constant velocity sees you, sitting at your desk, to be moving at a speed that is significant compared to $c$, yet somehow, you don't slip and fall. Whether or not a person walking on ice slips depends only on their motion with respect to the ice, so observer $B$ would not expect the man to slip based on his motion w.r.t. $B$, because his motion w.r.t. the ice is still the same.

Sandejo
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