Question

Constrained Repation
Explain string constant
steps for string constraint​

Answer 1

StrinG Constraint !!

When two objects are connected through a string and if the string have the following properties :-

• The length of the string remains constant. i.e., inextensible string.
• Always remains Tight , does not slàcks.

Then the parameters of the motion of the objects along the string and in the direction of extension have a definite Relation between them.

Steps For String Constraint !!

Step 1. :- Identify all the objects and number of strings in the problem.

Step 2. :- Assume variable to represent the parameters of motion such as displacement, velocity acceleration etc.

• Object which moves along a line can be specified by one variable.
• Objects moving in a plane are specfied by two variables.
• Objects moving in 3-D requires three variables to represent the motion.

Step 3. :- Identify a single string and divide it into different linear sections and write in the equation format :-

$l_{1} + l_{2} + l_{3} + l_{4} +l_{5} +l_{6} = l$

Step 4. :- Differentiate with respect to time.

$\frac{dl_{1}}{dt} + \frac{dl_{2}}{dt} + \frac{dl_{3}}{dt} + .... = 0$

$\frac{dl_{1}}{dt}$= represents the rate of increment of the portion 1, end points are always in contact with some object so take the velocity of the object Along the length of the string$\frac{dl_{1}}{dt} = v_{1} + v_{2}$

Take the positive sign if it tends to increase the length and negative sign if it tends to decrease the length. Here +V1 represents that upper end is tending to increase the length at rate V1 and lower end is tending to increase the length at rate V2.

Step 5. :- Repeat all above steps for different - different Strings.

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Here is a problem as an example :-

Let consider a problem given in attachment !!

Here

$l_{1} + l_{2} = constant$

$\frac{dl_{1}}{dt} + \frac{dl_{2}}{dt} = 0$

$( v_{1} - v_{p}) + (v_{p} - v_{2}) = 0</p><p>$

$v_{p} = \frac{v_{1 + v_{2}}}{2}$

Similarly,

$a_{p} = \frac{a_{1} + a_{2}}{2}$

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