0
19kviews
State D'Alembert's principle with two examples.
1 Answer
2
1.0kviews

D’alembert’s principle states that the sum of the differences between the forces acting on a mass particle and the rate of change of momentum of the system itself along any virtual displacement is zero.

i(Fimiai)δri=0 Fi=Net force acting on ith particle

mi=Mass of ith particle

ai=Acceleration of ith particle

ri= Virtual displacement of ith particle

Note:-In many textbooks, it is given as Fma=0, that is a special case (refer Wikipedia).

Note: Please ask your profs regarding what to write in the exams.

Example 1:-

Consider 2 teams playing tug-of-war. A box of mass ‘m’ is attached to a rope at two opposite places. Team A pulls the box with force FA and Team B pulls it with force FB. The force of Team A is more, so the box is accelerated towards Team A.

enter image description here

By D’alembert’s principle,

[FA+FB]ma=0

enter image description here

Example 2:-

A box of mass ‘m’ is kept on an inclined surface with co-efficient of friction µ and is accelerated downwards.

By D’alembert’s principle (along x-axis)

[-f+mg \sin\theta ]-ma=0 \\ i.e. \space -μ(mg \cos\theta )+ mg \sin\theta -ma=0

Please log in to add an answer.