Pulleys With Mass
There is a pulley of mass P with 2 blocks of respective masses a and b attached to different ends, and the ratio of masses is b : P : a = 1 : 2 : 3 .
Now, the blocks are set free and block a starts to drop with acceleration f = C g , where g is the acceleration due to gravity. What is the constant C ?
Note: The pulley is stationary but the disk inside the pulley can rotate.
The answer is 0.4.
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3 solutions
Call tension on left side of pulley is T1 And on right side pulley is T2
Let the masses have an acceleration a and pulley rotates with an angular acceleration b
Using Newton's Second law
3mg-T1 = 3ma
T2-mg = ma
Using torque equation for pulley
(T1-T2)R = mbR^2
Now we use the fact that the string isn't slipping on the pulley
a= Rb
Solving these system of equations = 2g/5
I also did the same way.
Didn't find your solution impressive. Should I show you how to write a solution by posting one?
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i dont want to make it impressive rather. just concept should be clear rather adding some fancy diagrams and explaining each and every step . and on the second note its rather a time waste for me (which i cannot afford at this point of time)
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Do not add such poor solutions if you don't have "time"
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@Anubhav Tyagi – It isn't a poor solution . it has got 4 upvotes!
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@Prakhar Bindal – come on @Anubhav Tyagi , does it really matter if neat diagrams are added and the concept matters ,i learnt a new concept from a such solution by him(of other problem) and now i am able to do questions of that type, moreover , i think solutions with "too much explanation" are pain in the neck ! i am writing it because it is coming in my notifications from ever since you guys are quarrelling over this little issue ! so, stop it now !
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@A Former Brilliant Member – Ignore the notifications and do not interfere
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@Anubhav Tyagi – let me say it clearly to you - DO NOT , i say, DO NOT TRY TO ACT BOSSY AROUND ME !
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@A Former Brilliant Member – Don't be too rude. The discussion was not meant for you and it was you who jumped inta it.
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@Anubhav Tyagi – look , it's not personal , i jumped into it just because it's coming in my notifications !
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@A Former Brilliant Member – You switch off your notifications Just do not disturb me by commenting again and again. MIND IT
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@Anubhav Tyagi – ohh ! like you are some great person ad i am just craving to talk to you , you lowlife maggot , and do not reply if you want to live in peace , little runt !
@Prakhar Bindal – Thats because other solutions are even worse
K . E . o f p u l l e y = 2 1 ∗ I ∗ ω 2 = 2 1 ∗ 2 1 ∗ m R 2 ∗ ω 2 = 2 1 ∗ ( 2 1 ∗ m ∗ V 2 ) . ∴ e q u i v a l e n t p u l l e y m a s s = 2 1 ∗ 2 = 1 . A c c e l e r a t i n g f o r c e = ( 3 − 1 ) g . e q u i v a l e n t m a s s a c c e l e r a t e d = a + P + b = 1 + 1 + 3 = 5 . N e w t o n ′ s 2 n d L a w 2 g = 5 f . f = 5 2 ∗ f = C ∗ f . S o C = 0 . 4