Solutions to I E Irodov - Physical Fundamentals of Mechanics

Newton single handedly brought about a new era in our understanding of the physical world, through his famous equation F = ma and the law of gravity. These laws successfully predict the behavior of all phenomena from the microscopic world to the astronomical world! Ofcourse, Einstien changed things once again but that was only after about 4 centuries. Solving Irodov dramatically helped me understand the power, elegance, simplicity and beauty of Physics. Hopefully you will enjoy the journey too.

Thursday, June 5, 2008

Irodov Problem 1.175

Suppose that after the collision masses m1 and m2 started moving at angles

and

a velocities v1 and v2 respectively as shown in the figure. Since there are no external forces, the momentum before and after collision will be conserved. Since it is an elastic collision initial and final energies will also be conserved. So we have,

From (1) and (2) we can obtain

From (3), (4) and (5) we have,

The maximum possible value of

is 1 since its a sine function. This means that the maximum possible value of

is given by,

The same result can also be obtained by using Lagrangian multipliers as follows,

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