Solution Found!
A mass m1 rests on a frictionless horizontal table.
Chapter 7, Problem 7.50(choose chapter or problem)
A mass m1 rests on a frictionless horizontal table. Attached to it is a string which runs hori-zontally to the edge of the table, where it passes over a frictionless, small pulley and down to where it supports a mass m2. Use as coordinates x and y the distances of mi and m2 from the pulley. These satisfy the constraint equation f (x, y)=--x-Fy=- const. Write down the two modified Lagrange equa-tions and solve them (together with the constraint equation) for x, 53, and the Lagrange multiplier X. Use (7.122) (and the corresponding equation in y) to find the tension forces on the two masses. Verify your answers by solving the problem by the elementary Newtonian approach.
Questions & Answers
QUESTION:
A mass m1 rests on a frictionless horizontal table. Attached to it is a string which runs hori-zontally to the edge of the table, where it passes over a frictionless, small pulley and down to where it supports a mass m2. Use as coordinates x and y the distances of mi and m2 from the pulley. These satisfy the constraint equation f (x, y)=--x-Fy=- const. Write down the two modified Lagrange equa-tions and solve them (together with the constraint equation) for x, 53, and the Lagrange multiplier X. Use (7.122) (and the corresponding equation in y) to find the tension forces on the two masses. Verify your answers by solving the problem by the elementary Newtonian approach.
ANSWER:Step 1 of 3
The following are given by the question:
The mass rest on the frictional table is 
The mass that is hanging with the of pulley is 
The constraint equation
The kinetic energy for
The potential energy for
The Lagrange equation is given by
Substitute the values and solve as
