# Homework Help: Person pulling a block physics

1. Jan 21, 2010

### atarr3

1. The problem statement, all variables and given/known data
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.

2. Relevant equations

Net force equations for static objects

3. 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.

Last edited: Jan 21, 2010
2. Jan 21, 2010

### aim1732

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).

3. Jan 21, 2010

### atarr3

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

4. Jan 21, 2010

### atarr3

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 $$tan\theta=\mu$$

5. Jan 22, 2010

### aim1732

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