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A 13552.2 N car traveling at 52.2 km/h rounds a curve of radius 1.68 multiplied by 102 m..

What is the minimum coefficient of static friction (μs) between the tires and the road that will allow the car to round the curve safely?

 May 12, 2014

Best Answer 

 #1
avatar+33614 
+5

Frictional force is given by $$F=\mu W$$ where μ is the coefficient of friction and W is the weight (13552.2N here).

The centripetal force required to prevent slipping is $$F=m\frac{v^2}{r}$$ where m is the mass (=W/g), v is speed and r is radius.

Equating these two forces we have: $$\mu W = \frac{W}{g}\frac{v^2}{r}$$  so  $$\mu = \frac{v^2}{gr}$$  

v = 52.2*103/3600 m/s, r = 1.68*102m and g = 9.81m/s2

$${\frac{{\left({\frac{{\mathtt{52\,200}}}{{\mathtt{3\,600}}}}\right)}^{{\mathtt{2}}}}{\left({\mathtt{9.81}}{\mathtt{\,\times\,}}{\mathtt{1.68}}{\mathtt{\,\times\,}}{\mathtt{102}}\right)}} = {\mathtt{0.125\: \!071\: \!265\: \!339\: \!299\: \!2}}$$

So  $$\mu = 0.125$$  approx.

 May 13, 2014
 #1
avatar+33614 
+5
Best Answer

Frictional force is given by $$F=\mu W$$ where μ is the coefficient of friction and W is the weight (13552.2N here).

The centripetal force required to prevent slipping is $$F=m\frac{v^2}{r}$$ where m is the mass (=W/g), v is speed and r is radius.

Equating these two forces we have: $$\mu W = \frac{W}{g}\frac{v^2}{r}$$  so  $$\mu = \frac{v^2}{gr}$$  

v = 52.2*103/3600 m/s, r = 1.68*102m and g = 9.81m/s2

$${\frac{{\left({\frac{{\mathtt{52\,200}}}{{\mathtt{3\,600}}}}\right)}^{{\mathtt{2}}}}{\left({\mathtt{9.81}}{\mathtt{\,\times\,}}{\mathtt{1.68}}{\mathtt{\,\times\,}}{\mathtt{102}}\right)}} = {\mathtt{0.125\: \!071\: \!265\: \!339\: \!299\: \!2}}$$

So  $$\mu = 0.125$$  approx.

Alan May 13, 2014
 #2
avatar+118608 
0

Thanks Alan.

 May 13, 2014

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