To determine The faster arrow will penetrate how much farther than the slower arrow. Explanation Given: The masses of two arrows are equal ( m 1 = m 2 ). The speed of one arrow is twice the other. The hay exerts a constant “frictional” force on the arrows. Formula used: From the Work-Energy Principle: Δ K + Δ U = W nc (1) Where: Δ K is the change in kinetic energy. Δ U is the change in potential energy. W nc is the work done by non-conservative forces. In this case is friction. Calculation: Equation (1) can be written as: 1 2 m v f 2 + m g h f = 1 2 m v i 2 + m g h i + W f (2) But, the arrows before and after impact are at the same height, therefore: 1 2 m v f 2 = 1 2 m v i 2 + W f (3) Now, the work done by friction ( W f ) is: W f = F f x cos ( 180 ° ) = − F f . Δ x (4) Inserting (4) into (3) we have: 1 2 m v f 2 = 1 2 m v i 2 − F f Δ x (5) When the arrows hit the hay, the final speed is zero: v f = 0 (6) Inserting (6) into (5): 0 = 1 2 m v i 2 − F f

7th Edition

ISBN: 9780321921741

Author: GIANCOLI

Publisher: PEARSON

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Static and Kinetic Friction

Kinetic friction comes into existence when there are moving surfaces means in other words we can say that the force which comes into existing between moving surfaces is known as kinetic friction.

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Chapter 6, Problem 17Q

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The faster arrow will penetrate how much farther than the slower arrow.

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Chapter 6, Problem 16Q

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