11/3/08 6:00 PM
MasteringPhysics
Page 1 of 15
http://session.masteringphysics.com/myct?productID=22377
[
Print View
]
Introductory mechanics
Chapter 08  Momentum, Impulse, And Collisions
Due at 11:59pm on Monday, October 27, 2008
View Grading Details
Center of Mass and External Forces
Learning Goal:
Understand that, for many purposes, a system can be treated as a pointlike particle with its mass
concentrated at the center of mass.
A complex system of objects, both pointlike and extended ones, can often be treated as a
point particle
, located at the system's
center of mass
. Such an approach can greatly simplify problem solving.
Before you use the center of mass approach, you should first understand the following terms:
System:
Any
collection of objects that are of interest to you in a particular situation. In many problems, you have a
certain freedom in choosing your system. Making a wise choice for the system is often the first step in solving the
problem efficiently.
Center of mass: The point that represents the "average" position of the entire mass of a system. The postion of the
center of mass
can be expressed in terms of the position vectors
of the particles as
.
The
x
coordinate of the center of mass
can be expressed in terms of the
x
coordinates
of the particles as
.
Similarly, the
y
coordinate of the center of mass can be expressed.
Internal force: Any force that results from an interaction between the objects inside your system. As we will show, the
internal forces do not affect the motion of the system's center of mass.
External force: Any force acting on an object inside your system that results from an interaction with an object outside
your system.
Consider a system of two blocks that have masses
and
. Assume that the blocks are pointlike particles and are located
along the
x
axis at the coordinates
and
as shown . In this
problem, the blocks can only move along the
x
axis.
Part A
Find the
x
coordinate
of the center of mass of the system.
Express your answer in terms of
,
,
, and
.
[
Print
]
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
11/3/08 6:00 PM
MasteringPhysics
Page 2 of 15
http://session.masteringphysics.com/myct?productID=22377
ANSWER:
=
Part B
If
, then the center of mass is located:
ANSWER:
to the left of
at a distance much greater than
to the left of
at a distance much less than
to the right of
at a distance much less than
to the right of
at a distance much greater than
to the right of
at a distance much less than
to the left of
at a distance much less than
Part C
If
, then the center of mass is located:
ANSWER:
at
at
halfway between
and
the answer depends on
and
Part D
Recall that the blocks can only move along the
x
axis. The
x
components of their velocities at a certain moment are
and
. Find the
component of the velocity of the center of mass
at that moment. Keep in mind that, in general:
.
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '10
 PICKETT
 Physics, Center Of Mass, Force, Kinetic Energy, Mass, Momentum, Velocity, Center of Mass and External Forces

Click to edit the document details