An engineer is trying to determine the maximum speed at which a vehicle travel around the curve without skidding. She know the coefficient of friction between the wheels and the road is 0.75 when the road is dry and 0.35 when the road is wet. She knows that the mass of the vehicle does not matter, but completes her calculations for a 900kg car.
Answer questions for the case when the car is traveling at the maximum speed that will allow it to navigate the in both wet and dry conditions.
Should she perform her calculations with the coefficient of friction for wet or day pavement?
In this case, what is the car's centripetal acceleration?
m/s2
In this case, what is the car's speed?
m/s
mph
Could vehicles, obeying a speed limit of 65mph, navigate the curve on wet or dry pavement?
do the wet of course
.35 m g = m Ac = m v^2/R
so v^2 = .35 *9.81 * R
You need to know R, the turn radius
In this case, the engineer should perform her calculations with the coefficient of friction for wet pavement since the maximum speed should be determined for the worst-case scenario.
To find the car's centripetal acceleration, we can use the formula:
Centripetal acceleration (a) = (v^2) / r
Where:
v = velocity (speed) of the car
r = radius of the curve
Assuming the engineer has the radius of the curve, we can substitute the values to calculate the centripetal acceleration.
To find the car's maximum speed, we need to use the centripetal acceleration and the coefficient of friction for wet pavement.
To determine if vehicles obeying a speed limit of 65mph can navigate the curve on wet or dry pavement, we need to compare the maximum speed calculated for both conditions with the speed limit.
To determine whether the engineer should perform her calculations with the coefficient of friction for wet or dry pavement, she needs to consider the worst-case scenario that ensures the safety of the vehicle. The lower coefficient of friction of 0.35 for wet pavement indicates less traction and potentially a higher risk of skidding. Therefore, it is advisable for the engineer to perform her calculations using the coefficient of friction for wet pavement.
Now, let's calculate the car's centripetal acceleration. Centripetal acceleration is given by the formula:
a = (v^2) / r
Where:
a is the centripetal acceleration,
v is the car's speed, and
r is the radius of the curve.
Since the question does not provide the radius of the curve, we cannot calculate the exact centripetal acceleration. However, we can proceed with the other calculations.
To find the car's speed, we need to use the equation for centripetal acceleration in terms of friction:
a = (v^2) / r = μ * g
Where:
μ is the coefficient of friction, and
g is the acceleration due to gravity (approximately 9.8 m/s^2).
Rearranging the equation, we get:
v = sqrt(μ * r * g)
For wet pavement, μ = 0.35.
Let's calculate the car's speed using this equation.
v_wet = sqrt(0.35 * r * 9.8)
Now, let's convert the car's speed from m/s to mph.
v_mph = v_wet * 2.23694
Next, we need to check if vehicles, obeying a speed limit of 65 mph, can navigate the curve on wet or dry pavement.
If the car's calculated speed (v_mph) is less than or equal to 65 mph, it can safely navigate the curve. Otherwise, it would be too fast, and the car would not be able to navigate the curve at the speed limit.
Keep in mind that the actual value of the car's speed and whether it can navigate the curve would depend on the specific radius of the curve, which is not provided in the question.