2019-03-01_Physics_Times

Constraint equations are relations between
displacements or velocities or accelerations of
different bodies connected together by strings &
pulleys and in contact with each other by being in
motion.

Applications

When we try to solve problems of physics with

the help of Newton’s laws or conservation of

energy or conservation of momentum, sometimes

the number of variables will be more than available

equations. In these cases, we look for constraint

relations which will help us in solving the unknown

variables.

If two surfaces have to be in contact with each
other then the components of velocities of the
two surfaces along the direction which is
perpendicular to two surfaces (normal direction)
must be same in magnitude and direction.
In the picture given below, the common normal
direction is shown with dotted line for different
bodies in contact.

Unless it is specified assume that the pulleys
and strings are massless and strings are
unstretchable.
(I) Distribution of tensions in strings

For a massless and unstretchable string and

massless pulley the tension will be always

distributed as follows.

(II) Velocities of different points on a string

If the string is unstretchable and tension in it is

non-zero then the tangential component of

velocities of the points (1) & (2) along the sense

of motion must be the same.

v v 1 t 2 t i.e v 1 cos 1 v 2 cos 2

v 1 cos 1 v 2 cos 2

If F1 2 3, ,F Fare the magnitudes of three forces

and   , , are the angle between forces

F 2



and F 3



,F 3 and and andF 1 F 1 F 2

   

respectively, as shown in figure. Then

according to Lami’s theorem

5. Constraint Equations

6. Wedge and block constraints

7. Pulley constraints

8. Lami’s theorem

F 1 F 2 F 3

sin sin sin

 

  