Explanation Given data: An air-track glider undergoes a perfectly inelastic collision with an identical glider that is initially at rest. Formula used: Write the expression for kinetic energy as follows. K = 1 2 m v 2 (1) Here, m is the mass of the object, and v is the speed (velocity) of the object. Write the expression for momentum of conservation for the given system. m 1 ( v 1 ) i + m 2 ( v 2 ) i = ( m 1 + m 2 ) v f (2) Here, m 1 is the mass of the first glider, m 2 is the mass of the second glider, ( v 1 ) i is the initial velocity (speed) of the first glider, ( v 2 ) i is the initial velocity of the second glider, and v f is the final velocity of the compound glider (after the collision both the gliders stick together). Explanation: From the given data, the collision is a perfectly inelastic collision. Therefore, both the gliders stick together after the collision and the energy is not conserved. But the momentum is conserved for the given system. Consider the mass of first glider ( m 1 ) as m . As the second glider is identical to the first glider, the mass of the second glider ( m 2 ) is also m . Consider the initial velocity of the fist glider ( v 1 ) i as v . As the second glider is initially at rest, the initial velocity of the second glider ( v 2 ) i is 0 m s . Rewrite the expression in equation (2) for the final velocity of the compound glider as follows. v f = m 1 ( v 1 ) i + m 2 ( v 2 ) i m 1 + m 2 Substitute m for m 1 , m for m 2 , v for ( v 1 ) i , and 0 m s for ( v 2 ) i . v f = ( m ) ( v ) + ( m ) ( 0 m s ) m + m = ( m ) ( v ) 2 m = 1 2 v Calculation of initial kinetic energy of the incident glider (first glider): Modify the expression in equation (1) for the initial kinetic energy of the incident glider (fist glider) as follows

College Physics: A Strategic Approach (3rd Edition)

3rd Edition

ISBN: 9780321879721

Author: Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field

Publisher: PEARSON

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Helmholtz Free Energy

The Helmholtz free energy is a thermodynamic potential used to calculate the measure of useful work from a closed system. This system is kept at constant temperature and volume. German physicist Hermann Helmholtz introduced this concept in 1882.

Question

Chapter 10, Problem 43P

To determine

To find: The fraction that the initial kinetic energy transformed into the thermal energy in the collision.

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Chapter 10 Solutions

College Physics: A Strategic Approach (3rd Edition)

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