Answered: Usually, we do not walk or even stand…

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

Usually, we do not walk or even stand on a lightweight boat or raft because of the danger of falling into the water. If you have ever stepped off a small boat onto a dock, however, you have probably noticed that the boat moves away from the dock as you step toward the dock or out of the boat. A heavy dog running on a long lightweight raft presents a similar situation. At first, the raft and the dog are at rest with respect to the water (see figure A below) so that

v_i = 0.

The dog then runs on top of the raft at

v_d = v_d

with respect to the water (see figure B below). The dog has one sixth the mass of the raft. Find an expression for the velocity of the raft after the dog began running. (Use the following as necessary: v_d.)

v_r =

Expert Solution

Step 1

This is a question regarding the moving of the center of mass.

For a two-body system, the velocity of the center of mass is given by the formula:
$Δ v_{C O M} = \frac{m_{1} Δ v_{1} + m_{2} Δ v_{2}}{m_{1} + m_{2}}$

where
$Δ v_{C O M}$ is the change in velocity of the center of mass.
$m_{1}$ is the mass of body 1
$Δ v_{1}$ is the change in velocity of body 1
$m_{2}$ is the mass of body 2
$Δ v_{2}$ is the change in velocity of body 2

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