Respuesta :
Answer:
Speed = 9.9 m/s
Explanation:
Given:
Coefficient of static friction is, [tex]\mu=0.25[/tex]
Radius of the curve, [tex]r=40[/tex] m
Let the speed that has to be reached be [tex]v[/tex] m/s.
In order to avoid sliding while making a turn, the frictional force provides the necessary centripetal force.
We know that, frictional force acting on a body is given as:
[tex]f=\mu N=\mu mg[/tex] ([tex]N=mg[/tex] as there is no vertical motion)
Also, from the definition of centripetal force,
[tex]f=\frac{mv^2}{r}[/tex]
On equating the above two equations, we get
[tex]\frac{mv^2}{r}=\mu mg\\v^2=\mu gr\\v=\sqrt{\mu gr}[/tex]
Now, plug in 0.25 for [tex]\mu[/tex], 9.8 for [tex]g[/tex] and 40 for [tex]r[/tex].
[tex]v=\sqrt{0.25\times 9.8\times 40}\\v=\sqrt{98}=9.9\textrm{ m/s}[/tex]
Therefore, speed of the car has to be slowed down to minimum of 9.9 m/s in order to avoid sliding while making a turn.
