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Fenixx
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Homework Statement
A sack of flour (mass m) can slide along a parabolic track i the vertical plane defined by y = [tex]\gamma[/tex]x2 The coefficient of (dynamic) friction is [tex]\mu[/tex]. You move this sack from x = 0 to x = x1 along the track by pulling it with a horizontal force F (you do this quasi-statically, i.e. the sack is not accelerated).
a) Calculate the work done by force F.
b) Discuss your result for the case [tex]\mu[/tex] = 0.
Homework Equations
Ffr=-[tex]\mu[/tex]mg
W = [tex]\int[/tex]F dl = F x cos [tex]\theta[/tex]
The Attempt at a Solution
I know that the horizontal force F = Ffr. If there were no frictional force, the work would simply be the change in gravitational potential from x to x1, correct? W = mg(y(x1) - y(x))
However, since there is a frictional force, and it is along a curved path, the work done actually depends on the path taken. I am not sure how to factor this part of the force in Since if F is horizontal, wouldn't amount of force that would affect the bag of flour would change with the path? Does this problem involve some type of line integral? I am not too familiar with this type of problem.
Any pointers in the right direction would be greatly appreciated. Thanks in advance for the help.