Finding max acceleration with force at angle incl friction

AI Thread Summary
To find the optimal angle for maximum acceleration of a 6kg block being pulled on a horizontal surface with a coefficient of kinetic friction of 0.15, the equations of motion and friction must be applied. The normal force is affected by the angle at which the force is applied, leading to a net force equation that includes friction. The solution involves taking the derivative of acceleration with respect to the angle and setting it to zero to find the maximum. Confusion arises regarding the expected values for the angle and the manipulation of the friction coefficient. The discussion emphasizes the importance of correctly applying physics principles to solve for the angle that maximizes acceleration.
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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)
Fnetx = Fcosθ - fk
ax = (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)
 
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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##.
 
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?
 
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##?
 
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
 
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