a. the maximum velocity at which a vehicle can go around a level curve is given by the formula v=√µrg, where µ is the coefficient of friction, r is the radius of the curve, and g is the acceleration due to gravity. explain how radical expression can be used to find the velocity for safe driving.
b. find the velocity of a vehicle which makes a turn without skidding if the radius of a circular turn is 20 meters, µ=0.6, g=9.8.
substitute in the values given and take the square root of your answer.
That will give you the max. safe velocity.
a. To find the velocity for safe driving around a level curve, we can use the given formula: v = õrg. Here's how the radical expression can be used:
1. Understand the variables:
- µ (mu): Coefficient of friction, which represents the grip between the tires and the road surface.
- r: Radius of the curve, which shows how sharp the turn is.
- g: Acceleration due to gravity, which is a constant value of 9.8 m/s² on Earth.
2. Substitute the given values:
- µ = 0.6 (from the information given)
- r = (the radius of the curve associated with the specific scenario)
- g = 9.8 m/s² (acceleration due to gravity on Earth)
3. Plug in the values:
- v = √(0.6 * r * 9.8)
4. Simplify the expression if needed:
- v = √5.88r (rounding up to 2 decimal places)
b. To find the velocity of the vehicle for a turn without skidding, we'll use the formula v = õrg and substitute the given values:
1. Substitute the values:
- µ = 0.6 (from the information provided)
- r = 20 meters (radius of the circular turn)
- g = 9.8 m/s² (acceleration due to gravity)
2. Plug in the values:
- v = √(0.6 * 20 * 9.8)
3. Calculate the expression:
- v = √117.6
- v ≈ 10.84 m/s (rounding up to 2 decimal places)
Therefore, the velocity of the vehicle for a turn without skidding is approximately 10.84 meters per second.