Radius of a Curve is 666.6m =R rate of superelevation is 8%= e=8/100 coefficient of side friction is 0.09…

Question

Radius of a Curve is 666.6m =R rate of superelevation is 8%= e=8/100 coefficient of side friction is 0.09. Find the speed in km/hr and m/s =U? g=9.8 Constant.

ScanSolve AI Tutor · Accepted Answer

This problem involves calculating the design speed for a horizontal curve on a highway, considering superelevation and the coefficient of side friction.

Identify the given values.
- Radius of the curve, $R = 666.6\, \text{m}$
- Rate of superelevation, $e = 8\% = \frac{8}{100} = 0.08$
- Coefficient of side friction, $f = 0.094$
- Acceleration due to gravity, $g = 9.8\, \text{m/s}^2$
State the formula for the design speed on a horizontal curve.
The formula that relates speed, radius, superelevation, and friction is:
$V = \sqrt{R g (e + f)}$
Where $V$ is the speed in meters per second (m/s).
Substitute the given values into the formula to find the speed in m/s.
$V = \sqrt{666.6\, \text{m} \times 9.8\, \text{m/s}^2 \times (0.08 + 0.094)}$ $V = \sqrt{666.6 \times 9.8 \times 0.174}$ $V = \sqrt{1137.92412}$ $V \approx 33.733\, \text{m/s}$
Convert the speed from m/s to km/hr.
To convert meters per second to kilometers per hour, multiply by $\frac{3600}{1000}$ or 3.6:
$V_{\text{km/hr}} = V_{\text{m/s}} \times 3.6$ $V_{\text{km/hr}} = 33.733\, \text{m/s} \times 3.6\, \text{km/hr per m/s}$ $V_{\text{km/hr}} \approx 121.439\, \text{km/hr}$
The speed is approximately $\boxed{\text{33.73 m/s}}$ or $\boxed{\text{121.44 km/hr}}$ .

Radius of a Curve is 666.6m =R rate of superelevation is 8%= e=8/100 coefficient of side friction is 0.09. Find the speed in km/hr and m/s =U? g=9.8 Constant.

Answer

Step-by-step solution

Identify the given values.

State the formula for the design speed on a horizontal curve.

Substitute the given values into the formula to find the speed in m/s.

Convert the speed from m/s to km/hr.

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