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"A car with mass m = 1000kg is traveling around a circular curve or radius r = 690 meters when it begins to rain.
The coefficients of static friction between the road and tires is μd = .64 when dry and μw = .23 when wet."

Q: What is the maximum tangential speed that the car can take the corner at w/o slipping when dry in m/s?
Q: When wet?

Respuesta :

Answer:

1. 65.78 m/s

2. 39.43 m/s

Explanation:

The centripetal force would be equal to force of friction.

[tex]\frac {mv^2}{R} = \mu mg[/tex]

where v is the tangential speed of the car, R is the radius of the curve and g is the acceleration due to gravity.

[tex] \Rightarrow v =\sqrt{\mu g R}[/tex]

1. For dry,

[tex]v = \sqrt{0.64 \times 9.8 m/s^2 \times 690 m} =65.78 m/s [/tex]

2. For wet,

[tex]v = \sqrt{0.23 \times 9.8 m/s^2 \times 690 m} =39.43 m/s[/tex]

abidemiokin

The maximum tangential speed that the car can take the corner at w/o slipping when dry is 65.82m/s

The maximum tangential speed that the car can take the corner at w/o slipping when wet is 39.46m/s

In order to get the maximum tangential speed of the car, we must know that the centripetal force would be equal to the force of friction.

The centripetal force is expressed as:

[tex]F_c=\frac{mv^2}{r}\\[/tex]

The force of friction is expressed as;

[tex]F_f=\mu R\\F_f= \mu mg[/tex]

Equating both expressions

[tex]F_c=F_f\\\frac{mv^2}{r} = \mu mg\\\frac{v^2}{r} = \mu g[/tex]

Given the following parameters

mass m = 1000kg

radius r = 690 meters

g = 9.81m/s²

[tex]\mu_d[/tex] = 0.64

[tex]\mu_w[/tex] = 0.23

Get the maximum tangential speed that the car can take the corner at w/o slipping when dry.

[tex]\frac{v^2}{r} = \mu_d g\\\frac{v^2}{690} =0.64(9.81)\\v^2=4,332.096\\v=\sqrt{4,332.096}\\v= 65.82 m/s[/tex]

Hence the maximum tangential speed that the car can take the corner at w/o slipping when dry is 65.82m/s

Get the maximum tangential speed that the car can take the corner at w/o slipping when wet.

[tex]\frac{v^2}{r} = \mu_d g\\\frac{v^2}{690} =0.23(9.81)\\v^2=1,556.847\\v=\sqrt{1,556.847}\\v= 39.46 m/s[/tex]

Hence the maximum tangential speed that the car can take the corner at w/o slipping when dry is 39.46m/s

Learn more here: https://brainly.com/question/13926507

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