I'm finishing up my week's assignment for my super-easy physics class and I must be having brain problems because out of nowhere this question has stumped me. The question concerns a curved road, which has a bank on the inside lane that is 5 degrees toward the center of the curve and on the OUTSIDE lane that is 5 degrees AWAY from the center.
The first part of the question had me find the radius of the curve that would be safe at 65mph if there were no friction. I found that to be 981.6m. The next part of the question asked me what the maximum safe speed for the outside lane if there's no friction. I answered that there is no safe speed if there's no friction on an outside bank, duh. 0 will still have you sliding away from the center.
Well, then it asks me what minimum coefficient of friction is to make the outside lane safe at the speed limit of 65mph. Now, I calculated this in the same way (basically) that I did the inside lane and ended up with a coefficient that is silly high, like more than 13.
Common sense tells me that this should be possible with a reasonable frictional coefficient, and when I plug in 0 degrees to my equation I still get a ridiculous high coefficient somewhere around 11. Soo...I'm pretty sure I made an algebra error, but this is the 11th time I've had to do this kind of thing on my homework and it's all starting to fuzz together and I can't find my error.
The equation I found is
Us=(-cosA(rg+v^2))/(sinA(v^2-rg))
Us = coefficient of friction
A = angle of bank (away from curve)
r = radius of curve
g = acceleration due to gravity
v = speed of vehicle around turn
Does anyone happen to know at a glance what I did wrong? Or at the very least, you can make fun of me and discuss physics.
EDIT: standby, I think I found the error, i may have switched a cos - sin into a sin - cos.
The first part of the question had me find the radius of the curve that would be safe at 65mph if there were no friction. I found that to be 981.6m. The next part of the question asked me what the maximum safe speed for the outside lane if there's no friction. I answered that there is no safe speed if there's no friction on an outside bank, duh. 0 will still have you sliding away from the center.
Well, then it asks me what minimum coefficient of friction is to make the outside lane safe at the speed limit of 65mph. Now, I calculated this in the same way (basically) that I did the inside lane and ended up with a coefficient that is silly high, like more than 13.
Common sense tells me that this should be possible with a reasonable frictional coefficient, and when I plug in 0 degrees to my equation I still get a ridiculous high coefficient somewhere around 11. Soo...I'm pretty sure I made an algebra error, but this is the 11th time I've had to do this kind of thing on my homework and it's all starting to fuzz together and I can't find my error.
The equation I found is
Us=(-cosA(rg+v^2))/(sinA(v^2-rg))
Us = coefficient of friction
A = angle of bank (away from curve)
r = radius of curve
g = acceleration due to gravity
v = speed of vehicle around turn
Does anyone happen to know at a glance what I did wrong? Or at the very least, you can make fun of me and discuss physics.
EDIT: standby, I think I found the error, i may have switched a cos - sin into a sin - cos.
Warhead[97]