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physics 2211
MP09: Chapter 9
Due at 5:30pm on Monday, October 22, 2007
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Momentum and Internal Forces
Learning Goal:
To understand the concept of total momentum for a system of objects and the effect of the
internal forces on the total momentum.
We begin by introducing the following terms:
System:
Any collection of objects, either pointlike or extended. In many momentumrelated problems, you have a
certain freedom in choosing the objects to be considered as your system. Making a wise choice is often a crucial step
in solving the problem.
Internal force:
Any force interaction between two objects belonging to the chosen system. Let us stress that both
interacting objects must belong to the system.
External force:
Any force interaction between objects at least one of which does not belong to the chosen system;
in other words, at least one of the objects is external to the system.
Closed system:
a system that is not subject to any external forces.
Total momentum:
The vector sum of the individual momenta of all objects constituting the system.
In this problem, you will analyze a system composed of two blocks, 1 and 2, of respective masses
and
. To
simplify the analysis, we will make several assumptions:
The blocks can move in only one dimension, namely, along the
x
axis.
1.
The masses of the blocks remain constant.
2.
The system is closed.
3.
At time
, the
x
components of the velocity and the acceleration of block 1 are denoted by
and
. Similarly,
the
x
components of the velocity and acceleration of block 2 are denoted by
and
. In this problem, you will
show that the total momentum of the system is not changed by the presence of internal forces.
Part A
Find
, the
x
component of the total momentum of the system at time
.
Express your answer in terms of
,
,
, and
.
ANSWER:
=
Part B
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MasteringPhysics: Assignment Print View
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10/21/07 4:15 PM
Find the time derivative
of the
x
component of the system's total momentum.
Hint B.1 Finding the derivative of momentum for one block
Consider the momentum of block 1:
. Take the derivative of this expression with respect to time,
noting that velocity is a function of time, and mass is a constant:
.
Hint B.2 The relationship between velocity and acceleration
Recall the definition of acceleration as
.
Express your answer in terms of
,
,
, and
.
ANSWER:
=
Why did we bother with all this math? The expression for the derivative of momentum that we just obtained will be
useful in reaching our desired conclusion, if only for this very special case.
Part C
The quantity
(mass times acceleration) is dimensionally equivalent to which of the following?
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 Fall '08
 DUNCAN
 Physics, Energy, Kinetic Energy, Momentum, Potential Energy, chuck

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