Finding max acceleration with force at angle incl friction

[YearnToLearn]

Homework Statement

Hey. I was doing some exam practice questions, but I hit a snag with this one and can't quite work out how to proceed.

A 6kg block at rest is pulled along a horizontal surface by force F→ at angle θ. Given that the coefficient of kinetic friction is 0.15, find the optimal angle at which to apply the force to achieve maximum acceleration.

Homework Equations

F = ma
fk = μkN
F→² = F²sin²θ + F²cos²θ

The Attempt at a Solution

N = mg - Fsinθ
μk = 0.15/58.86
fk = (2.55×10^-3)(mg-Fsinθ)
Fnet_x = Fcosθ - fk
a_x = (Fcosθ - fk)/m

From here I guess I need to form a differential equation and solve for maximum but this leads to θ being a ridiculous angle. Any advice? (P.S, sorry if this is in the wrong section, still trying to gauge the levels of physics being done in each)

 

[Delta2]

You just have to take the derivative of ##a_x## with respect to ##\theta## and set it to 0 and solve the equation involving ##\theta##, that is to solve ##\frac{da_x}{d\theta}=0##.

 

[YearnToLearn]

Still getting a weird value for θ while solving for the maximum. Will work through and check my values, but can we confirm that the logic is sound?

 

[Delta2]

Do you get ##tan(\theta)=\mu_k## at the end? Why is this weird, since the friction coeeficient is small we expect theta to be small also (if friction coefficient was zero it would be theta=0 as can be understood easily).

There is something i don't understand why you divide 0.15 / 58.86 for ##\mu_k##?

 

[YearnToLearn]

My bad. Playing catch up at the moment and only started looking at this concept today. Another look at the derivative and I can see the manipulation. Thanks for the help