Answered: Four objects are situated along the y…

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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Question

Four objects are situated along the y axis as follows: a 1.97-kg object is at +2.93 m, a 2.95-kg object is at +2.53 m, a 2.42-kg object is at the origin, and a 4.08-kg object is at -0.509 m. Where is the center of mass of these objects?
x =
y =

Expert Solution

Step 1

Given that,

the masses of four objects are

$m_{1} = 1.97 (k g) m_{2} = 2.95 (k g) m_{3} = 2.42 (k g) m_{4} = 4.08 (k g)$

And each mass is placed on the y-axis, their positions are

$P_{1} = (x_{1}, y_{1}) = (0, 2.93 (m)) P_{2} = (x_{2}, y_{2}) = (0, 2.53 (m)) P_{3} = (x_{3}, y_{3}) = (0, 0 (m)) P_{4} = (x_{4}, y_{4}) = (0, - 0.509 (m))$

Since the center of mass of the system of particles is at

$\begin{array}{rcl} r & = & \frac{m_{1} r_{1} + m_{2} r_{2} + m_{3} r_{3} + . . . . . .}{m_{1} + m_{2} + m_{3} + . . . . . .} \\ = & \frac{\sum_{i} m_{i} r_{i}}{\sum_{i} m_{i}} \\ = & \frac{\sum_{i} m_{i} r_{i}}{M} \end{array}$

where r₁, r₂,... is the position of the masses m₁,m₂,... respectively, and M is the total mass of the system.

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