Question

A 1900 kg car rounds a curve of radius 84.0 m banked at an angle of 11°. What is the maximum speed that the car can reach without skidding if the coefficient of static friction between the tires and the road is 0.68?

Answer 1

The maximum speed of the car is 10.43 m/s.

Step-by-step explanation:

Given that,

Mass of the car, m = 1900 kg

Radius of the curve, r = 84 m

Angle of banking,
`\theta=11^(\circ)`

The coefficient of static friction between the tires and the road is 0.68. We need to find the maximum speed of the car. It is given by :

`v=√(\mu r g\tan\theta)`

`v=√(0.68* 84* 9.8* \tan(11))`

v = 10.43 m/s

So, the maximum speed of the car is 10.43 m/s. Hence, this is the required solution.

Answer 2

The maximum speed is 28.79 m/s.

Step-by-step explanation:

Given that,

Mass of car = 1900 kg

Radius = 84.0 m

Angle = 11°

Coefficient static friction = 0.68

We need to calculate the maximum speed

Using formula of maximum speed

`v_(max)=(rg*(\sin\theta+\mu\cos\theta)/(\cos\theta-\mu\sin\theta))^{(1)/(2)}`

Where, r = radius

g = acceleration due to gravity

Put the value into the formula

`v_(max)=(84.0*9.8*(\sin11+0.68*\cos11)/(\cos11-0.68*\sin11))^{(1)/(2)}`

`v_(max)=28.79\ m/s`

Hence, The maximum speed is 28.79 m/s.