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# A 175-g glider on a horizontal, frictionless air track is ISBN: 9780321675460 31

## Solution for problem 37E Chapter 14

University Physics | 13th Edition

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Problem 37E

A 175-g glider on a horizontal, frictionless air track is attached to a fixed ideal spring with force constant 155 N/m. At the instant you make measurements on the glider, it is moving at 0.815 m/s and is 3.00 cm from its equilibrium point. Use energy ?conservation to find (a) the amplitude of the motion and (b) the maximum speed of the glider. (c) What is the angular frequency of the oscillations?

Step-by-Step Solution:

Solution 37E Step 1: Introduction : In this question ,we need to find the amplitude of the motion In the second part we need to find the maximum speed of the glider In the third part we need to find the angular frequency of the oscillations Data given Mass of the glider m = 175 g = 0.175 kg Force constant k = 155 N/m Velocity v = 0.815 m/s Distance x = 3.0 cm Step 2 : When the glider is at rest, all the energy stored in the glider accomplies to potential energy PE Whereas when the glider is moving with maximum velocity, the energy of the glider is given by Kinetic energy Hence using law of conservation of energy we have KE = PE We can write this as KE = 1/2 mv and PE = 1/2 kx 2 Since the total energy E of the system is given by E = 1/2 mv + 1/2 kx 2 Substituting values we get E = 1/2 × 0.175 kg × (0.815 m/s) + 1/2 × 155 N/m × (0.03 m) 2 E = 0.0581 J + 0.06975J E = 0.12785 J This can be approximated to E = 0.128 J Hence we have the total energy of the glider as 0.128 J Step 3 : We can obtain the amplitude using A = 2E/K Substituting values we get A = 2 × 0.128 J)/ 155 N/m A = .65 × 10 3 A = 0.0406 m This can be written as A = 4.06 cm Hence we have the amplitude as 4.06 cm

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##### ISBN: 9780321675460

The full step-by-step solution to problem: 37E from chapter: 14 was answered by , our top Physics solution expert on 05/06/17, 06:07PM. Since the solution to 37E from 14 chapter was answered, more than 1219 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: University Physics, edition: 13. This full solution covers the following key subjects: glider, horizontal, angular, attached, conservation. This expansive textbook survival guide covers 26 chapters, and 2929 solutions. The answer to “A 175-g glider on a horizontal, frictionless air track is attached to a fixed ideal spring with force constant 155 N/m. At the instant you make measurements on the glider, it is moving at 0.815 m/s and is 3.00 cm from its equilibrium point. Use energy ?conservation to find (a) the amplitude of the motion and (b) the maximum speed of the glider. (c) What is the angular frequency of the oscillations?” is broken down into a number of easy to follow steps, and 72 words. University Physics was written by and is associated to the ISBN: 9780321675460.

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