Here's the Second Harry Potter Question!
If the image is not clearly visible, No problem! All the details are given in the question
Harry's wand is threatened again, and this time Hermione must save it!
The wand was kept on a rough table (with friction coefficient 1) with one third of the total length on the table and the rest free. Assuming the mass of the rod is m kg, determine at what maximum angle rotated by the wand (shown by x in the image) will Hermione have to shout "arresto momenta" to save the wand from sliding on the table ?
Give your answer as the value of tan(x) .
Assumptions: Assume that "Arresto Momenta" stops the wand giving ample time to Hermione to go and handle the wand, thereby saving it from sliding on the table.
The answer is 0.5.
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2 solutions
Moderator note:
Can you explain why your equations describe the moment the wand loses contact? In other words, what distinguishes your constraints from a generic point in the movement of the wand?
@Kishore S Shenoy Check the solution. Since it was quite long,I posted it's snapshot.
One thing, I used θ in place of x as mentioned in the problem.
Challenge Master: In the solution above, I have used F r i c t i o n = μ s m a x × N o r m a l R e a c t i o n , where μ s m a x is the maximum possible coefficien of static friction available, and hence it is the limiting case , after which the rod will start sliding.
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Great! In general, I would add more of your thought your process to your solutions, it makes them much more transparent to everyone else. Terrific problem and solution.
@Abhijeet Verma I am sorry, I get it, I should never use ω = 0 since it will slip at the limiting case and we have to find that case. I get my mistake. Thanks @Brilliant Physics and Abhijeet !
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No problem. Keep up the good work.
@Abhijeet Verma and @Pulkit Deshmukh Try these questions A long Slipway! and Slippery Pulley
Good work @Abhijeet Verma
@AbhijeetVerma I hated the harry potter part
@Pulkit Deshmukh this is the way to tag a name
@Abhijeet Verma Can you explain how you got the answer?
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Surely, I will post my solution tomorrow. Btw, can you please post the solution to the problem collision gallore.
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I don't know. The solution will be highly complex in algebra right?
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@Kishore S. Shenoy – Kishore S Shenoy You seem to be good in Mechanics You should try https://brilliant.org/problems/thats-why-i-like-physics/?group=sjTfEiwDY8IV&ref_id=963793
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@Pulkit Deshmukh – And you try A very edgy problem!
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@Kishore S. Shenoy – What do you mean by "when its centre of mass is in the horizontal line of the edge".I solved the rest of the part
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@Pulkit Deshmukh – When the centre of mass of the cylinder is in line with the Edge horizontally. i.e. R dist traveled down by CM
@Pulkit Deshmukh – Is my above solution right?
@Pulkit Deshmukh – Is it a circle?
@Abhijeet Verma Try this question A very edgy problem!
Where is the first Harry Potter question?
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@Kishore S. Shenoy – All questions posted by me are in the set Problems I Posted
Is this a solution?