+0  
 
0
157
1
avatar+104 

A stone is dropped at t = 0. A second stone, with twice the mass of the first, is dropped from the same point at 100ms.

 

(a) How far below the release point is the center of mass of the two stones at t=300? (Neither stone has yet reached the ground.)

(b) How fast is the center of mass of the two-stone system moving at that time?

Kreyn  Mar 23, 2017
Sort: 

1+0 Answers

 #1
avatar+732 
+2

Solution(s)

 

\(\text {(a) }\\ \text {Find coordinates (y) for masses } \displaystyle m_1(y_1) \text { and } m_2(y_2)\\ y_1 = 0.5(9.81)*(0.300)^2 = 0.441 \small \text{meters}\\ y_2 = 0.5(9.81)*(0.300 – 0.100)^2 = 0.196 \small \text{ meters}\\ \\ \small \text{ Formula for the center of mass (2 objects):}\\ \\ y_{com} = \dfrac{(m_1y_1 + m_2y_2)}{(m_1 + m_2)}\\ y_{com} = \dfrac{((1) (0.441) + (2)(0.196)}{(1) + (2)} = 0.278 \small \text{ meters} \leftarrow \small\color{green} \text{Answer for (a)}\\ \text {(b) }\\ \text{Velocity of center of mass}\\ v1=(g)(t)_1 = 9.8*0.300 = \small \text{ 2.94m/s }\\ v2=(g)(t)_2 = 9.8*0.200 = \small \text{ 1.96m /s }\\ v_{com} = \dfrac{((1)(2.94)+(2)(1.96))}{3} = 2.287 \small \text{ m/s} \leftarrow \small\color{green} \text{Answer for (b)}\\\\ \small \text{ }\\ \small \text{Theory & Formulas: Complements of Archimedes of Syracuse, Leonhard Euler, Sir Isaac Newton, Pappus of Alexandria,}\\ \small \text{Guido Ubaldi, Francesco Maurolico, Federico Commandino, Simon Stevin, Luca Valerio, Jean-Charles de la Faille, Paul Guldin,}\\ \small \text{John Wallis, Louis Carré, Pierre Varignon, and Alexis Clairaut.}\\ \small \text{ } \hspace{20em} \scriptsize \text {(Probably a few others, too. The COM concept is ancient) }\\ \small \text{Produced by Lancelot Link and company. }\\ \small \text{Directed by GingerAle. }\\ \small \text{Sponsored by Naus Corp. Quantum Pharmaceuticals. }\\ \small \text{ } \hspace{15em} \scriptsize \text { Making a better world by neutralizing the quantum dumbness of }\\ \small \text{ } \hspace{15em} \scriptsize \text { Blarney Masters and related dumb-dumbs }\\\)

GingerAle  Mar 24, 2017

36 Online Users

avatar
avatar
avatar
avatar
avatar
avatar
avatar
avatar
avatar
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details