1. The problem statement, all variables and given/known data
Using the relation ## tan \theta = \mu_k ## what angle should the rope make with the horizontal
in order to minimize the work done per unit distance traveled along the ground.
2. Relevant equations
## W = Fdcos\phi ##
3. The attempt at a solution
I found ## tan\theta = \mu_k ## by finding the derivative of a with respect to ##\theta ## and let it equal 0.
## a = \frac{F}{m}cos\theta - \mu_k (g - \frac{F}{m}sin\theta) = 0 ##
I think ## F = \mu_k F_N ## is a minimum when ## \frac{dF}{dx} = 0 ## and ##\frac{d^2F}{dx^2} > 0 ## . Is this correct? If so how do I use this?
Using the relation ## tan \theta = \mu_k ## what angle should the rope make with the horizontal
in order to minimize the work done per unit distance traveled along the ground.
2. Relevant equations
## W = Fdcos\phi ##
3. The attempt at a solution
I found ## tan\theta = \mu_k ## by finding the derivative of a with respect to ##\theta ## and let it equal 0.
## a = \frac{F}{m}cos\theta - \mu_k (g - \frac{F}{m}sin\theta) = 0 ##
I think ## F = \mu_k F_N ## is a minimum when ## \frac{dF}{dx} = 0 ## and ##\frac{d^2F}{dx^2} > 0 ## . Is this correct? If so how do I use this?
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