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# THE ELEMENTARY MATHEMATICAL MODELS AND BASIC CONCEPTS OF MATHEMATICAL MODELING

DOI link for THE ELEMENTARY MATHEMATICAL MODELS AND BASIC CONCEPTS OF MATHEMATICAL MODELING

THE ELEMENTARY MATHEMATICAL MODELS AND BASIC CONCEPTS OF MATHEMATICAL MODELING book

# THE ELEMENTARY MATHEMATICAL MODELS AND BASIC CONCEPTS OF MATHEMATICAL MODELING

DOI link for THE ELEMENTARY MATHEMATICAL MODELS AND BASIC CONCEPTS OF MATHEMATICAL MODELING

THE ELEMENTARY MATHEMATICAL MODELS AND BASIC CONCEPTS OF MATHEMATICAL MODELING book

## ABSTRACT

Here m v2/ 2 is the kinetic energy of a bullet of mass m and velocity v , M is the mass of a load, V is the velocity of the system “bullet-load” immediately after the collision, g is the free-fall acceleration, I is the length of the rod, a is the angle of the maximal shift. The required velocity is determined by the formula ____________________

which will be quite exact, if one neglects the losses of energy on the heating up of the bullet and load, the resistance of the air, the speeding up of the rod, etc. These at first sight reasonable assumptions are actually incorrect. The processes occurring at the “merging” of the bullet and the pendulum, are no longer purely mechanical. Therefore when calculating the value v , the law of conservation of mechanical energy is not valid: the total energy, rather than the mechanical one is conserved. It provides only the lower limit for the estimation of the velocity of the bullet (for the correct solution of this

F ig .l.