Questions 7 through 9 pertain to the situation described below:Two balls of masses, 1.00 kg and 3.00 kg, respectively, are connected by a light spring of springconstant 81.0N/m and set on a smooth, horizontal table.(7) What is the reduced mass of this two-body system?(A) 0.75 kg; (B) 1.00 kg; (C) 1.50 kg; (D) 2.25 kg; (E) 3.00 kg.(8) What is the period of oscillations of the two balls along the spring?(A) 0.305 s; (B) 0.405 s; (C) 0.505 s; (D) 0.605 s; (E) 0.705 s.(9) What is the maximum relative speed between the two balls if the spring is stretched by27.0 cm with the two balls released from rest?(A) 2.01 m/s; (B) 2.21 m/s; (C) 2.41 m/s; (D) 2.61 m/s; (E) 2.81 m/s.

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Description: Questions 7 through 9 pertain to the situation described below:Two balls of masses, 1.00 kg and 3.00 kg, respectively, are connected by a light spring of springconstant 81.0N/m and set on a smooth, horizontal table.(7) What is the reduced mass of th

7. Find the reduced mass of the two body system. μ=m1m2m1+m2=1.00 kg3.00 kg1.00 kg+3.00 kg=0.75 kg…

Answered: Questions 7 through 9 pertain to the…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Step 1

Find the reduced mass of the two body system.

$\begin{array}{rcl} μ & = & \frac{m_{1} m_{2}}{m_{1} + m_{2}} \\ = & \frac{(1.00 kg) (3.00 kg)}{(1.00 kg + 3.00 kg)} \\ = & 0.75 kg \end{array}$

Therefore, the correct option is (A) 0.75 kg.

Find the period of oscillation of the two balls along the spring.

$\begin{array}{rcl} T & = & 2 π \sqrt{\frac{μ}{k}} \\ = & 2 (3.14) \sqrt{\frac{0.75 kg}{81.0 N/m}} \\ = & 0.605 s \end{array}$

Therefore, the correct option is (D) 0.605 s.

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