Osvaldo Apodaca

2021-12-19

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

Charles Benedict

Beginner2021-12-20Added 32 answers

Given data:

$r=80\text{}m$

$\theta ={15}^{\circ}$

a) the ideal speed of car$v}_{1$

The velocity$v}_{1$ is given by

$\mathrm{tan}\theta =\frac{{v}_{1}^{2}}{r\cdot g}$

$v}_{1}=\sqrt{r\cdot g\cdot \mathrm{tan}\theta$

$v}_{1}=\sqrt{80\times 9.8\times \mathrm{tan}\left(15\right)$

$v}_{1}=14.49\text{}\frac{m}{s$

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$v}_{1$

${F}_{1}=m{a}_{1}=\frac{m{\left({v}_{1}\right)}^{2}}{r}=\frac{m{\left(14.49\right)}^{2}}{80}=2.62\text{}m$

the centripetal force acting on the car for speed$v}_{2}=25\text{}k\frac{m}{h}=6.94\text{}\frac{m}{s$

${F}_{2}=m{a}_{2}=\frac{m{\left({v}_{2}\right)}^{2}}{r}=\frac{m{\left(6.94\right)}^{2}}{80}=0.6\text{}m$

the frictional force acting due to the centripetal force

$f=|{F}_{1}-{F}_{2}|$

on substituting the respective values

${\mu}_{k}\cdot m\cdot g=2.02\text{}m$

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

${\mu}_{k}=0.206$

a) the ideal speed of car

The velocity

b) where the coefficient of friction

We know force of friction of given by

the centripetal force acting on the car for speed

the centripetal force acting on the car for speed

the frictional force acting due to the centripetal force

on substituting the respective values

22+64

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