(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Straight out of the book: "An initially stationary box of sand is to be pulled across a floor by means of a cable in which the tension should not exceed 1100N. The coefficient of static friction between the box and the floor is 0.35. (a) What should be the angle between the cable and the horizontal in order to pull the greatest possible amount of sand and (b) what is the weight of the sand and box in that situation?"

2. Relevant equations

F = ma

F_{s}= μ_{s}F_{N}

3. The attempt at a solution

So, I've decided that the x component, that is, the 1100N (I call this F_{c}) times cosθ, has to be equal to static friction. If it wasn't, then more sand could be added until it was (is this an incorrect assumption?). From there I tried to solve it like my professor has been doing by analzying the sum of the forces in the x direction and y direction separately to try to get two equations with two variables. The idea then would be that it would be an algebra problem, but I keep getting three unknowns (F_{N}, F_{g}, and θ). I'll go ahead and show my work, I am probably going something wrong or going about it the wrong way (if I wasn't, this problem would have been done long ago).

Ʃ F_{x}= F_{c}Cosθ - F_{s}= 0

Or

F_{c}Cosθ = μ_{s}F_{N}

Ʃ F_{y}= F_{c}Sinθ + F_{N}- F_{g}= 0

or

F_{c}Sinθ + F_{N}= F_{g}

So, I don't know θ, F_{N}, or F_{g}and I don't see any third equation that I can use to eliminate a variable. Do I have to set the y component of F_{c}to something like I did the x component? Or was that my mistake from the beginning? Also, I will probably be spamming this forum with physics problems, sorry and if there is a limit do say. But I am tired of struggling with these homework problems, and the professor's hours are kind of awkward for me.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: How to find the angle that will pull the most weight

**Physics Forums | Science Articles, Homework Help, Discussion**