Automobile Centripetal acceleration

[bearhug]

The cornering performance of an automobile is evaluated on a skidpad, where the maximum speed that a car can maintain around a circular path on a dry, flat surface is measured. Then the centripetal acceleration is calculated as a multiple of "g", the free-fall acceleration due to gravity at the Earth's surface. The main factors affecting the performance are the tire and the suspension of the car. A Dodge Viper GTS can negotiate a skidpad of radius 58 m at 89 km/h. Calculate the centripetal acceleration due to static friction for this maneuver.

89km/h= 24.7m/s

Originally the first equation that pops into my head is a=v^2/r. However what's throwing me off is how the problem says that accerleration is a multiple of g (9.8). Then it also mentions to calculate the accleration due to static friction fs. Is the coefficient of static friction at all relevant to this problem? All the other equations I've looked at involve the coefficient which is also what's confusing me.

 

[Doc Al]

Originally the first equation that pops into my head is a=v^2/r. However what's throwing me off is how the problem says that accerleration is a multiple of g (9.8).

You have the right equation. To express the acceleration in terms of g, just divide your answer by 9.8 m/s^2. (Example: If the acceleration were 19.6 m/s^2, that would be 2 g's.)

Then it also mentions to calculate the accleration due to static friction fs. Is the coefficient of static friction at all relevant to this problem? All the other equations I've looked at involve the coefficient which is also what's confusing me.

Static friction is producing the centripetal force, but that's just background info. All you need to do is calculate the acceleration.

 

[kyle8921]

I would approach this problem by first understanding the concept of centripetal acceleration and its relationship to circular motion. Centripetal acceleration is the acceleration towards the center of a circular path, and it is caused by the centripetal force, which is provided by the friction force in this case.

To calculate the centripetal acceleration, we can use the formula a = v^2/r, where v is the velocity and r is the radius of the circular path. In this case, the velocity is 24.7 m/s and the radius is 58 m, so the centripetal acceleration would be (24.7)^2/58 = 10.5 m/s^2.

Now, we need to calculate the centripetal force, which is provided by the friction force. In this case, the friction force is the static friction force, as the car is not slipping on the surface. The maximum static friction force can be calculated using the formula fs = μsN, where μs is the coefficient of static friction and N is the normal force (equal to the weight of the car). Since the problem does not provide the coefficient of static friction, we cannot calculate the exact value of the friction force.

However, we can estimate the minimum coefficient of static friction needed to maintain the given speed and radius. Using the formula v^2 = μsrg, where g is the acceleration due to gravity (9.8 m/s^2), we can rearrange the equation to solve for μs. Plugging in the given values, we get μs = v^2/rg = (24.7)^2/(58*9.8) = 0.107.

Therefore, the minimum coefficient of static friction needed for the Dodge Viper GTS to maintain a speed of 89 km/h around a circular path with a radius of 58 m is 0.107. This value can be used to further evaluate the tire and suspension performance of the car, as they are the main factors affecting the maximum speed and centripetal acceleration in this maneuver.