Question

The maximum speed around a level curve is 30.0 km/h. What is the maximum speed around a curve with twice the radius?

Answer 1

Answer:

When the radius is doubled, its speed will be 42.42 km/h.

Explanation:

Given that,

The maximum speed around a level curve is 30 km/h = 8.34 m/s

We need to find the maximum speed around a curve with twice the radius. The maximum speed of the object is given by :

$v=\sqrt{\mu rg}$............(1)

If radius is doubled, r' = 2r

The maximum speed is given by :

$v'=\sqrt{\mu r'g}$

$v'=\sqrt{\mu (2r)g}$..........(2)

Dividing equation (1) and (2) we get :

$\dfrac{v}{v'}=\dfrac{1}{\sqrt2}$

$v'=\sqrt{2} v$

$v'=\sqrt{2}\times 30$

v' = 42.42 km/h

So, when the radius is doubled, its speed will be 42.42 km/h. Hence, this is the required solution.

Answer 2

Answer:

The maximum speed around a curve is 42.4 km/h.

Explanation:

Given that,

Maximum speed = 30.0 km/h

New radius = 2 r

The centripetal force will be same for both situation.

We need to calculate the new maximum speed around a curve

Using formula of  centripetal force

$\dfrac{mv^2}{r}=\dfrac{mv^2}{r}$

Put the value into the formula

$\dfrac{v^2}{2r}=\dfrac{30^2}{r}$

$v=30\sqrt{2}\ km/h$

$v=42.4\ km/h$

Hence, The maximum speed around a curve is 42.4 km/h.