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invariant99
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Homework Statement
This question was posed on a recent test I had to write. Our professor does not let us keep our graded tests nor does she share solutions, so all I have is the problem statement. I've made an effort to recreate the solution I had, but I got it wrong in any case and I'd like to understand the problem better.
A car drives around a mountain on a frictionless path that is bank outwards. Assume the car's wheels still have traction. The car's route traces out a horizontal circle. Is this possible? Explain your reasoning.
Here is the image that was provided to us:
Homework Equations
Let theta be the angle of the banked path from horizontal axis. I used:
- F_{Earth on car} = mg
- F_{road on car} = mg * cos(theta)
- F_{traction} = u_{kinetic} * F_{road on car} = u_{kinetic} * mg * cos(theta) = 0
The Attempt at a Solution
I started by creating a free-body diagram of the forces acting on the car. I drew F_{traction} as a dashed line because I'm not sure if it belongs there. I'm confused about how the path can be frictionless, but the wheels can still have traction. That makes no sense to me. I listed it as F_{traction} = 0 above, but I would like verification and clarification on this matter.
From here, I considered the forces along the horizontal and vertical.
F_{net, x} = -F_{road on car} * cos(theta) + F_{traction} * cos(theta)
= -mg * cos(theta) * cos(theta) + 0
= -mg * cos(theta) * cos(theta)
F_{net, y} = F_{road on car} * sin(theta) - F_{Earth on car}
= mg * cos(theta) * sin(theta) - mg
= 0
At this point I got stuck, but I don't think that continuing with these calculations is going to help me. Nor am I convinced that these calculations are correct. Any advice?