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 θ with the plane, then the magnitude of the force is

F=(μW/(μsin(θ)+cos(θ)))

Where μ is a positive constant called the coefficient of friction and where 0≤θ≤π/2. Find the value for tanθ which minimizes the force. Your answer may depend on W and μ, but use "u" instead of μ when entering your answer.

Question

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 θ with the plane, then the magnitude of the force is

F=(μW/(μsin(θ)+cos(θ)))

Where μ is a positive constant called the coefficient of friction and where 0≤θ≤π/2. Find the value for tanθ which minimizes the force. Your answer may depend on W and μ, but use "u" instead of μ when entering your answer.

anonymous · Answer

Since $F=\frac{\mu W}{\mu sin \theta + cos \theta}$
You simply differentiate it in terms of $\theta$ and find the minimum value of F. Do you need further help?