A car goes along the circular curve of radius 30 m. If the road is banked at an angle of015 withthe horizontal, calculate the maximum speed in m/s at which the car can travel without skid.
Question
A car goes along the circular curve of radius 30 m. If the road is banked at an angle of015 withthe horizontal, calculate the maximum speed in m/s at which the car can travel without skid.
Solution
To solve this problem, we need to use the physics concept of banking of roads and the formula for maximum speed without skidding.
The formula is given by:
v_max = sqrt(rg*tanθ)
where:
- v_max is the maximum speed without skidding,
- r is the radius of the curve,
- g is the acceleration due to gravity, and
- θ is the angle of banking.
Given:
- r = 30 m,
- θ = 15 degrees, and
- g = 9.8 m/s² (approximate value).
First, we need to convert the angle from degrees to radians because the trigonometric functions in the formula work with radians.
θ = 15 * (π/180) = 0.2618 radians
Now, we can substitute the values into the formula:
v_max = sqrt(30 m * 9.8 m/s² * tan(0.2618 radians))
Calculating the value of tan(0.2618 radians) gives approximately 0.2679.
So,
v_max = sqrt(30 m * 9.8 m/s² * 0.2679)
v_max = sqrt(78.42 m²/s²)
v_max = 8.86 m/s
Therefore, the maximum speed at which the car can travel without skidding is approximately 8.86 m/s.
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