A car rounds an unbanked curve with a radius of curvature 40 m. The coefficient of friction between the tires?A car rounds an unbanked curve with a radius of curvature 40 m. The coefficient of friction between the tires and the road is 0.6. What is the maximum speed the car can travel without slipping? This is a homework question. Thank you guys for any help you can offer :) | |
Use the centripetal force and Newton's Law of Motions then! We know that...
r = 40
µ_s = 0.6
It's best to draw the diagram since it helps you answer the question and understands what is going on!
Here is how the problem works if a car is on a banked curve.
F_ncos(θ) = F_nsin(θ)µ_s + mg
F_nsin(θ) + F_ncos(θ)µ_s = mv²/r
Since θ = 0, we have...
F_n = F_n * 0 * µ_s + mg
F_n * 0 + F_n * 1 * µ_s = mv²/r
F_n * µ_s = mv²/r
Since F_n = mg...
mg * µ_k = mv²/r
gµ_k = v²/r
v = √(grµ_s)
Therefore...
v = √(9.81 * 40 * 0.6)
≈ 15.3 m/s
Good luck!
