A car enters a 300-m radius horizontal curve on a rainy day when the coefficient of static friction between its tires and the road is 0.300. What is the maximum speed at which the car can travel around this curve without sliding?
A car enters a 300-m radius horizontal curve on a rainy day when the coefficient of static friction between its tires and the road is 0.300. What is the maximum speed at which the car can travel around this curve without sliding?
Answer:
The maximum speed at which the car can travel around this curve without sliding is 29.69 [tex]\frac{m}{s}[/tex]
Explanation:
Given:
Coefficient of static friction [tex]\mu_{s} = 0.300[/tex]
Radius of curve [tex]r = 300[/tex] m
Here in our question car move in circular path so force is given by,
From the formula of centripetal force,
[tex]F = \frac{mv^{2} }{r}[/tex]
Where [tex]F =[/tex] Normal force
[tex]\mu_{s} N = \frac{mv^{2} }{r}[/tex]
[tex]\mu_{s} mg = \frac{mv^{2} }{r}[/tex]
Where [tex]g = 9.8 \frac{m}{s^{2} }[/tex]
[tex]\mu_{s} g = \frac{v^{2} }{r}[/tex]
[tex]v= \sqrt{\mu_{s} g r}[/tex]
[tex]v = \sqrt{0.30 \times 9.8 \times 300}[/tex]
[tex]v = 29.69 \frac{m}{s}[/tex]
Therefore, the maximum speed at which the car can travel around this curve without sliding is 29.69 [tex]\frac{m}{s}[/tex]