- #1
NewbiNewton
- 5
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If a curve with a radius of 88m is perfectly banked for a car traveling 75km/h, what must be the coefficient of static friction for a car not to skid when traveling at 95km/h?
Relevent equations: F=ma, Fr=muFN
FNsintheta=m(v2/radius) = mg/costheta x sintheta = m(v2/r) = mgtantheta = m(v2/r) = tantheta = v2/rg
I got as far as determining the angle at 75km/h(20.8m/s), which is about 26.4 degrees. I tried to go further and solve the components of the forces of FN and mg, but I had some difficulties, and even if I had done those correctly, I didn't know how to solve the components of the frictional force. I did see this problem fully worked out on another website, but I could not follow the approach. I was confused by certain things they did. Such as giving a vertical component to friction, for which I thought has no vertical component. I would greatly appreciate it if the problem was worked out for me, and then I can ask questions about the steps that were taken. I have been trying to work this problem out for a couple of days, so I'm looking forward to understanding it finally.
Thank you in advance.
Relevent equations: F=ma, Fr=muFN
FNsintheta=m(v2/radius) = mg/costheta x sintheta = m(v2/r) = mgtantheta = m(v2/r) = tantheta = v2/rg
I got as far as determining the angle at 75km/h(20.8m/s), which is about 26.4 degrees. I tried to go further and solve the components of the forces of FN and mg, but I had some difficulties, and even if I had done those correctly, I didn't know how to solve the components of the frictional force. I did see this problem fully worked out on another website, but I could not follow the approach. I was confused by certain things they did. Such as giving a vertical component to friction, for which I thought has no vertical component. I would greatly appreciate it if the problem was worked out for me, and then I can ask questions about the steps that were taken. I have been trying to work this problem out for a couple of days, so I'm looking forward to understanding it finally.
Thank you in advance.