A curve of radius 76 m is banked for a design speed of 100 km/h. If the coefficient of static friction is 0.38 (wet pavement), at what range of speeds can a car safely make the curve? [Hint: Consider the direction of the friction force when the car goes too slow or too fast.]

Question

rvc · Answer

r= 76m
v= 100 km/h --> 100 X 5/18 m/s
$\mu$= 0.38

anonymous · Answer

@rvc it needs a max and a min /:

michele_laino · Answer

on our car are acting two forces, namely:
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michele_laino · Answer

the condition for v_max, is then:
$$\Large  m\frac{{{v^2}}}{R} = \mu mg$$

michele_laino · Answer

which comes from the subsequent condition:
$$\Large  {F_{centrifugal}} = {F_{friction}}$$

michele_laino · Answer

solving the last expression for v, we get:
$$\Large  {v_{\max }} = \sqrt {\mu Rg} $$

michele_laino · Answer

actually our curve is, like below:
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rvc · Answer

v^2=  r g tan $\theta$

michele_laino · Answer

we have this vector decomposition:
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