- 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 y-component 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 y-component 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 y-component of F (now equal to P) to mg, so (F * sin9,9 + m*g) and letting this be the y-component 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 x-component. 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.