Explanation Given data: Initial speed of the hockey puck ( v i ) is 5.0 m s . Coefficient of kinetic friction between the puck and ice ( μ ) is 0.05. Formula used: The only force due to friction works on the puck and this frictional work on the puck is equal to the change in the kinetic energy. Therefore, write the expression for conservation of energy for the given conditions as follows. W f = Δ K (1) Here, W f is the work done by the friction, and Δ K is the change in kinetic energy of the puck. Write the expression for work done by the friction. W f = F f d cos θ (2) Here, F f is the kinetic friction force , d is the displacement (distance travelled by the puck), and θ is the angle between frictional force and direction of displacement. Write the expression for kinetic friction force. F f = μ m g (3) Here, μ is the coefficient of kinetic friction, m is the mass of the puck, and g is the acceleration due to gravity, which is 9 .8 m s 2 . Write the expression for change in kinetic energy of the puck. Δ K = K f − K i (4) Here, K i is the initial kinetic energy of the puck, and K f is the final kinetic energy of the puck. Write the expression for kinetic energy. K = 1 2 m v 2 (5) Here, m is the mass of the object, and v is the velocity (speed) of the object. Explanation: Consider the mass of the puck as m . From the given data, it is clear that the, the direction of frictional force on the puck is opposite to the direction of motion (or displacement). Therefore, the angle between the direction of frictional force and the displacement ( θ ) is 180 ° . Calculation of work done by kinetic friction force: From equation (3), substitute μ m g for F f in equation (2). W f = μ m g d cos θ Substitute 0.05 for μ , m for m , 9 .8 m s 2 for g , and 180 ° for θ . W f = ( 0.05 ) ( m ) ( 9 .8 m s 2 ) d cos ( 180 ° ) = 0.49 m d ( − 1 ) m s 2 = − 0.49 m d m s 2 Calculation of initial kinetic energy: Modify the expression in equation (5) to find the initial kinetic energy of the puck as follows. K i = 1 2 m ( v i ) 2 Substitute m for m , and 5.0 m s for v i

College Physics: A Strategic Approach Technology Update, Books a la Carte Plus Mastering Physics with Pearson eText -- Access Card Package (3rd Edition)

3rd Edition

ISBN: 9780134201979

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 38P

To determine

To find: The distance travelled by the puck before it comes to rest.

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Chapter 10 Solutions

College Physics: A Strategic Approach Technology Update, Books a la Carte Plus Mastering Physics with Pearson eText -- Access Card Package (3rd Edition)

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The distance travelled by the puck before it comes to rest.

Solution Summary: The author explains how to write the expression for conservation of energy for the given conditions, such as the initial speed of the puck, the coefficient of friction, and the angle between frictional force and direction of displacement.

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To find: The distance travelled by the puck before it comes to rest.

Chapter 10 Solutions