Coefficient of friction and tension

[lax1113]

Homework Statement

This is sort of a multi part question which had us do a lab. We did the lab and got numbers, and from this we have to make an equation to find exact values that we could use to find the angle for which a block can be pulled, with a certain coefficient of friction, that the tension in the string will be least.

Homework Equations

we solved an equation to get T=(k*mg)/(cos(/)+sin(/)*k)
So basically, for each value of K, what angle of theta... (/)... makes T the least

Cant figure out how to make the symbol for friction coefficient, so for now K= kinetic coefficient of friction.

The Attempt at a Solution

So far I have decided that when the coefficient of friction is greater than 1, the best angle is going to be over 45 degrees. When it is less than 1, the best angle is under 45 degrees, and when it is 1, the best angle is 45. This is because to make T the least, the bottom of the fraction has to be the most. if the coefficient is more than 1, the sin will be made greater by the angle being over 45 degrees, so the higher the coefficient, the more important it is to take advantage of an increasing sin value with an increasing degree. So with that being said, I am going to make a graph of many values and see where that leads, but is there a way to solve this without graphing, stricly analytically.

 

[tiny-tim]

… we solved an equation to get T=(k*mg)/(cos(/)+sin(/)*k)
So basically, for each value of K, what angle of theta... (/)... makes T the least

Hi lax1113!

(have a theta: θ and a phi: φ and a mu: µ )

You're trying to minimise or maximise cosθ + µsinθ.

Hint: Find a φ so that this is proportional to cos(θ + φ) or sin(θ + φ).