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Colt1911 [192]
2 years ago
14

A car is driving around a banked curve, with the road surface at an angle of 10.0º. If the radius of curvature of the road is 30

.0 m and the coefficient of static friction between the tires of the car and the road is 0.65, what is the maximum speed (in km/hr) the car can go without skidding?
Physics
1 answer:
IRISSAK [1]2 years ago
7 0

Answer:

maximum speed 56 km/h

Explanation:

To apply Newton's second law to this system we create a reference system with the horizontal x-axis and the Vertical y-axis. In this system, normal is the only force that we must decompose

       sin 10 = Nx / N

      cos 10 = Ny / N

      Ny = N cos 10

     Nx = N sin 10

Let's develop Newton's equations on each axis

X axis

We include the force of friction towards the center of the curve because the high-speed car has to get out of the curve

     Nx + fr = m a

     a = v2 / r

     fr = mu N

     N sin10 + mu N = m v² / r

     N (sin10 + mu) = m v² / r

Y Axis  

     Ny -W = 0

     N cos 10 = mg

Let's solve these two equations,

    (mg / cos 10) (sin 10 + mu) = m v² / r

    g (tan 10 + μ / cos 10) = v² / r

    v² = r g (tan 10 + μ / cos 10)

They ask us for the maximum speed

   v² = 30.0 9.8 (tan 10+ 0.65 / cos 10)

   v² = 294 (0.8364)  

   v = √(245.9)

   v = 15.68 m / s

Let's reduce this to km / h

   v = 15.68 m / s (1 km / 1000m) (3600s / 1h)

   v = 56.45 km / h

This is the maximum speed so you don't skid

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Marta_Voda [28]

Answer:

see below

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Now, correlation.  The definition of correlation in statistics is any statistical relationship between two random variables or data.  This simply means that these two events are connected to one another.  A POSITIVE correlation is when two correlated events move in the same direction as one another.  I have added a graph to help visualize this.  In this problem as the gas is pressed harder, the acceleration increases.  If the pressure on the pedal was decreased, then the acceleration also decreases.  If the pressure on the pedal is constant, the the acceleration is constant.

I hope this helps!

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