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String Pulley Constraints are very commonly used in high school physics and mainly comes under Newton’s Laws of motion (NLM). This concepts are frequently asked in exams such as JEE Mains and even JEE Advanced !!
Time becomes an important factor in such competitive examinations, especially JEE Mains.
Index :
- How to apply the trick
- Easy examples
- Moderate-Difficult Examples
1. How to apply ?
Remember the rules :
- Only one string at a time
- On the string –> ‘minus’ sign (Recall the -ve charge sign on ions from chemical bonding because that’s how I kept it in my mind)
- Away from the string –> ‘plus’ sign
How to use it in problems ? (Have patience...Lot of things will get easier for you)
Steps :
- Mark the points on the string such that whole string is covered (starting to end)
- For pulleys, mark for the points- where the string first comes in contact with the pulley (pt 2) and where the string leaves the contact with pulley (pt 3)
- Now start from one end,( say pt1) . The relation will be as follows :
-Va + 0 + 0 +Vb
Why ?
-Va because Va is going on the string
+0 because pt2 is connected to pulley and pulley is at rest
+0 pt3 is connected to pulley and pulley is at rest
+Vb because pt4 is connected to block B and Vb is going away from the string
4. Finally equate everything to zero
-Va + 0 + 0 +Vb = 0
Va = Vb
2. Easy Examples :
Q.1 Write down the constraint relation between velocities of block A and block B by referring the image of setup alongside.
Solution :
Constraint relation can be written as : (Applying trick, starting from block A)
Q.2 Write down the constraint relation between velocities of block A and block B by referring the image of setup alongside.
Solution :
We start from block A (Just move along the string one-by-one) :
Q.3 Write down the constraint relation between velocities of block A and block B by referring the image of setup alongside.
Solution : Let’s start from block A
Moderate to Difficult Examples :
Solution : Part(a) –
(Lets start from the point near the rigid support)
Part (b) : Again we start from the point attached to the rigid end
(Note that the derivative of velocity wrt time is acceleration. So once you get the velocity constraint relation, just taking its derivative wrt time will give you the constraint relation for accelerations)
Q. Give the constraint relations between block A and block B in the setup shown in image alongside
Solution:
Recall that this trick can only be applied to one string at a time !
So, we take velocity of pulley X as Vx as shown in figure below and we start applying trick from block A end
But, we need relations between Vb and Va
Q. Next Example :
Solution :
As we discussed, only the velocity component along the string are to be considered
Starting from star (*) mark
Same approach, mark all the points on the string first
But, we know that the value of Vb (RHS) from the above expression is always going to be positive since
So, the assumed direction of Vb (upwards) is also correct !
Conclusion :
So, over here, we end this article. Do practice some more string pulley constraint problems using this trick. But also don’t miss out on the actual procedure. Tricks should always be your secondary option !!
We will keep coming up with more such articles to help you in your preparation !! Thank you for your time.
All the very Best !!
