This is the full question. Please help.
If a curved road with radius of 95 m is properly banked for a car traveling at 65 km/h (the angle of the ramp which arrows for the car traveling at 65 km/h safely without help from static friction please refer to the figure below), what must be the coefficient of the static friction for a car not to skid when traveling at 95 km/h?
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The coefficient of static friction for a car not to skid when traveling on a curved road at 95 km/h can be calculated using the formula:
coefficient of static friction = (V^2 / R) * (sin(theta))
where V is the speed of the car in meters per second, R is the radius of the curved road in meters, and theta is the angle of the ramp.
First, we need to convert the speed of the car from km/h to m/s. To do this, we can use the formula:
V (m/s) = V (km/h) * (1000 m / 1 km) * (1 h / 3600 s)
For a car traveling at 65 km/h, this gives us a speed of 65 * (1000 / 1) * (1 / 3600) = 18.0556 m/s.
Next, we need to find the angle of the ramp that allows a car to travel safely on the curved road at this speed without help from static friction. We can use the formula:
tan(theta) = (V^2 / R) * (g)
where V is the speed of the car in meters per second, R is the radius of the curved road in meters, and g is the acceleration due to gravity (which is approximately 9.8 m/s^2 on Earth).
For a car traveling at 18.0556 m/s on a curved road with a radius of 95 m, this gives us an angle of theta = tan^-1((18.0556^2 / 95) * 9.8) = 7.17 degrees.
Finally, we can use this angle to calculate the coefficient of static friction for a car traveling at 95 km/h (which is equivalent to 26.3889 m/s) on the curved road. Substituting the values into the formula above, we get:
coefficient of static friction = (26.3889^2 / 95) * (sin(7.17)) = 0.6108
Therefore, the coefficient of static friction for a car not to skid when traveling on the curved road at 95 km/h must be approximately 0.6108.