Question

A sport car of m=2,000lb moving with velocity v=160mph must make a U-turn on pavement with friction coefficient of μ_s=0.5. In what (a) minimal turn radius and (b) minimal time can the driver make the turn without losing speed and skidding? Why do Formula-1 race car drivers sacrifice a lot of driving time by replacing tires so often when racing?

Answer 1

Answer:

a) R = 3441.6 ft  and b)    t = 46 s

Explanation:

a) Let's use Newton's second law, where acceleration is centripetal

X axis

     fr = ma

     a = v² / R

Y Axis

    N-W = 0

    N = W = mg

The friction force formula is

    fr = μ N

Let's replace and calculate

    μ mg = m v² / R

    R = v² / mu g

Reduce the units

    g = 32 ft / s2

    v = 160 m / h (5280 ft / 1 mile) (1h / 3600s) = 234.66 ft / s

    R = 234.66² / (0.5 32)

    R = 3441.6 ft

b) With the car going at constant speed (speed module) we can use

     v = d / t

Where is going to make a U-turn this is half a circle, then let's find the length of the circle and the distance is half

      L = 2π R

      d = ½ 2π R = π R

      d = π 3441.6

      d = 10812 ft

Let's calculate the time

       t = d / v

       t = 10812 / 234.66

       t = 46 s

Formula 1 riders have to change their tires frequently because the wear coefficient of friction decreases significantly, which would force them to take the curves more slowly

Answer 2

According to question (A) R = 3441.6 ft and (B)  t = 46 s

What is Newton's second law?

Newton’s second law another name is a law of force and also acceleration. Newton’s second law of motion explains how force can change the acceleration of the object and also how acceleration and also that mass of the same object are related.

a) Then Let's use Newton's second law, whereas acceleration is centripetal

Then X-axis

After that, fr = ma

Then, a = v² / R

No, Y-Axis is

Then N-W = 0

After that N = W = mg

Then The friction force formula is

fr = μ N

Now, Let's replace and also calculate

Then μ mg = m v² / R

After that R = v² / mu g

Then Reduce the units

The unit of g is = 32 ft / s2

  $v = 160 m / h (5280 ft / 1 mile) (1h / 3600s) = 234.66 ft / s$

  $R = 234.66² / (0.5 32)$

  $R = 3441.6 ft$

b) Then With the car going at a constant speed (speed module) we can use

Then v = d / t

Where is going to make a U-turn this is half a circle, then let's find the length of the circle and also the distance is half

Then L = 2π R

After that d = ½ 2π R = π R

Then d = π 3441.6

$d = 10812 ft$

Now Let's calculate the time

     $t = d / v$

     $t = 10812 / 234.66$

      $t = 46 s$

The Formula 1 riders have to change their tires frequently because the wear coefficient of friction decreases significantly, which would have been forcing them to take the curves more slowly.

Find out more information about Newton's second law here

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