 #1
Crunge
 11
 4
 Homework Statement:

A box with the mass m is carried by a truck. The truck is driving in a slanted curve with the speed v. The radius of the curve is ρ and its slope is at the angle θ. There is friction between the box and the truck, and the box is not moving. Calculate using the gravitational acceleration g = 9,806.
What is the maximal normal force if the static friction coefficient (μs) is 0,434, m is 5,8 kg and θ is 9,9°?
 Relevant Equations:
 Maximal friction force (Fmax) = μs * N
The problem that I immediately ran into was how I would calculate N without knowing Fmax. I didn't think the ycomponent of N would simply be the same magnitude as mg. After being stuck for a good while I even tested if it was, by dividing the magnitude of mg with cosθ, which of course ended up being wrong. The ycomponent of Fmax would have to be taken into consideration as well, but to calculate Fmax I wanted to use the formula Fmax = μs * N, and since N is also unknown I was stumped again. I then realized the existence of the force P. After snooping around in our study material I found a formula that seemed relevant to this situation and which was similar to Fmax = μs * N. According to this, P = μs * mg. However, even after calculating P I'm still not sure what conclusions I can draw about F or N. At first I just tried assuming that F is equal to P but in the opposite direction, however this seemed a bit pointless since then they would take out each other in regards to equilibrium and not affect N right? I decided to ignore P and try my original plan of adding the ycomponent of F (now equal to P) to mg, so (F * sin9,9 + m*g) and letting this be the ycomponent of N. Divide that by cos9,9 and I get real close (If rounded down to the proper amount of significant figures it's even correct) but I could see that I had gone about it wrong. I then noticed that in the example for P = μs * mg, P and mg are perpendicular. So I let the old value for P merely be the xcomponent. Divide that by cos9,9 and I get a new slightly larger value for P. This brought me even closer to the right answer but as espected it is still wrong. After all I'm pretending that P has somehow vanished after F has been calculated. I don't think I can simply let F and P be of equal magnintude, but as long as both F and N are unknown I don't know where to get anymore crucial information out of the problem. This is where I am currently stuck.