# Person pulling a block physics

## Homework Statement

A person pulls on a block with a force F, at an angle theta with respect to the horizontal. The coefficient of friction between the block and the ground is mu. For what theta is the F required to make the block slip a minimum.

## Homework Equations

Net force equations for static objects

## The Attempt at a Solution

So I'm pretty sure I've got all of my equations right, but I'm having trouble simplifying my results further.
$$Ff=\mu N$$ when the box slips and $$N=Mg-Fsin\theta$$ Substitution gives $$\mu\left(Mg-Fsin\theta\right)=Fcos\theta$$ I don't know how to solve for theta.

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For theta for minimum F, write F as an explicit function of theta and differentiate w.r.t theta. Put it equal to zero(the calculus concept of maxima and minima).

But I'm not trying to find the minimum F, I'm trying to find the minimum theta.

Ok I think I have it now. I maximize the denominator in $$F=\frac{\mu Mg}{cos\theta+\mu sin\theta}$$ so the derivative is $$\mu cos\theta-sin\theta=0$$ So $$tan\theta=\mu$$

As an afterthought, don't you think the minimum theta is zero?