 # f a car takes a banked curve at less than the ideal speed, friction is Osvaldo Apodaca 2021-12-19 Answered

f a car takes a banked curve at less than the ideal speed, friction is needed to keep it from sliding toward the inside of the curve (a real problem on icy mountain roads). (a) Calculate the ideal speed to take a 80 m radius curve banked at $15.0\cdot$. (b) What is the minimum coefficient of friction needed for a frightened driver to take the same curve at 25.0 km/h?

You can still ask an expert for help

• Live experts 24/7
• Questions are typically answered in as fast as 30 minutes
• Personalized clear answers

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it Charles Benedict
Given data:

$\theta ={15}^{\circ }$
a) the ideal speed of car ${v}_{1}$
The velocity ${v}_{1}$ is given by
$\mathrm{tan}\theta =\frac{{v}_{1}^{2}}{r\cdot g}$
${v}_{1}=\sqrt{r\cdot g\cdot \mathrm{tan}\theta }$
${v}_{1}=\sqrt{80×9.8×\mathrm{tan}\left(15\right)}$

b) where the coefficient of friction $\mu$
We know force of friction of given by
$f={\mu }_{k}\cdot N={\mu }_{k}\cdot m\cdot g$
the centripetal force acting on the car for speed ${v}_{1}$

the centripetal force acting on the car for speed

the frictional force acting due to the centripetal force
$f=|{F}_{1}-{F}_{2}|$
on substituting the respective values

${\mu }_{k}=\frac{2.02}{9.8}=0.206$
${\mu }_{k}=0.206$

We have step-by-step solutions for your answer!