alleryThe least coefficient of friction letting a car take an unbanked curve of radius $r$ at speed $v$ is:
- $\mu=\dfrac{v^2}{rg}$
- $\mu=\dfrac{gr}{v^2}$
- $\mu=\dfrac{v^2}{r}$
- $\mu=\dfrac{v}{rg}$
Show answer and solution
Correct answer: A. $\mu=\dfrac{v^2}{rg}$
1. On an unbanked curve, friction alone supplies the centripetal force.
2. So $\mu mg=\dfrac{mv^2}{r}$, since the maximum friction available is $\mu mg$.
3. The mass cancels from both sides.
4. Rearranging gives $\mu=\dfrac{v^2}{rg}$.
5. Dropping the $g$ leaves $\dfrac{v^2}{r}$, which is an acceleration and not dimensionless; inverting gives $\dfrac{gr}{v^2}$. Both were recorded errors.
_Source: NECTA ACSEE 2023 Physics 131/1, Question 3: Mechanics (Uniform Circular Motion)_