MasteringPhysics: Assignment Print View
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10/4/2007 4:06 PM
PHCC 141: Physics for Scientists and Engineers I - Fall 2007
6b. Work, Energy, and Power
Due at 11:59pm on Monday, October 1, 2007
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Integrate Force to Find Work
Work Done by a Spring
Consider a spring, with spring constant
, one end of which is attached to a wall. The spring is initially unstretched, with the
unconstrained end of the spring at position
The spring is now compressed so that the unconstrained end moves from
. Using the work integral
find the work done
the spring as it is compressed.
Spring force as a function of position
The spring force vector
as a function of displacement
from the spring's equilibrium position, is given by
is the spring constant and
is a unit vector in the direction of the displacement of the spring (in this case, towards the
Integrand of the work integral
The work done by the spring is given by the integral of the dot product of the spring force and an infinitesimal displacement of
the end of the spring:
where the infinitesmal displacement vector
has been written as
in terms of given quantities, and then compute
the dot product to find an expression for the integrand. (Note,
Express your answer in terms of