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ace123
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[SOLVED] minimum and maximum values
An object with weight W is dragged along a horizontal plane by a force acting along a rope attached to the object. If the rope makes an angle [tex]\vartheta[/tex] with the plane, then the magnitude of the force is
F= Z(W)/Z sin [tex]\vartheta[/tex] + cos [tex]\vartheta[/tex]
Where Z is a positive constant called the coeffecient of friction where 0< Z<[tex]\pi[/tex]/2.
Show that F is minimized when tan [tex]\vartheta[/tex] =Z
The theorem's I am allowed to use:
The extreme value theorem
Fermat's theorem
I don't really understand what the problem is asking me. What do they mean by F is minimized? Maybe if I knew that I could do it.
An object with weight W is dragged along a horizontal plane by a force acting along a rope attached to the object. If the rope makes an angle [tex]\vartheta[/tex] with the plane, then the magnitude of the force is
F= Z(W)/Z sin [tex]\vartheta[/tex] + cos [tex]\vartheta[/tex]
Where Z is a positive constant called the coeffecient of friction where 0< Z<[tex]\pi[/tex]/2.
Show that F is minimized when tan [tex]\vartheta[/tex] =Z
The theorem's I am allowed to use:
The extreme value theorem
Fermat's theorem
I don't really understand what the problem is asking me. What do they mean by F is minimized? Maybe if I knew that I could do it.