The graphical and symbolic representations
for four different vector fields are shown below. Match the graphical and
symbolic representations.
Explain how vectors and dot products
can be used to calculate the work done when a force moves an object along a path described by a position vector
. Under what circumstances can movement take place without doing
any work?
Consider the two dimensional vector
field with the symbolic representation
Describe (in words) a closed curve that will give positive work if
represents the force acting and your curve
represents the path that the object moves along. Do the same for negative
work.
Summarize what you have learned
about the relationship between the curve, the vector field and the sign of
the work done. Give plausibility arguments for your conclusions, using what
you have learned about approximating work by use of collections of straight
line segments and sums.
Describe a procedure for calculating
the work done by a force acting on an object that moves along a
path parameterized by , with .