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Friction Coefficient between Wheels and Road Surface using Retardation on Front Wheel Formula

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Friction Coefficient Between Wheels And Ground BFW is the friction coefficient which is generated between wheels and ground when the brakes are applied. Check FAQs

μ = a \cdot \frac{b}{[g] \cdot x \cdot \cos (θ) + a \cdot h}

μ - Friction Coefficient Between Wheels And Ground BFW?a - Braking Retardation BFW?b - Vehicle Wheelbase BFW?x - Horizontal Distance of C.G. From Rear Axle BFW?θ - Road Inclination Angle BFW?h - Height of C.G of Vehicle BFW?[g] - Gravitational acceleration on Earth?

Friction Coefficient between Wheels and Road Surface using Retardation on Front Wheel Example

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Here is how the Friction Coefficient between Wheels and Road Surface using Retardation on Front Wheel equation looks like with Values.

Here is how the Friction Coefficient between Wheels and Road Surface using Retardation on Front Wheel equation looks like with Units.

Here is how the Friction Coefficient between Wheels and Road Surface using Retardation on Front Wheel equation looks like.

0.58 = 3.0191 \cdot \frac{2.4}{9.8066 \cdot 1.3 \cdot \cos (12) + 3.0191 \cdot 0.0075}

0.58 = 3.0191m/s² \cdot \frac{2.4m}{9.8066m/s² \cdot 1.3m \cdot \cos (12°) + 3.0191m/s² \cdot 0.0075m}

0.58 = 3.0191 \cdot \frac{2.4}{9.8066 \cdot 1.3 \cdot \cos (12) + 3.0191 \cdot 0.0075}

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Friction Coefficient between Wheels and Road Surface using Retardation on Front Wheel Solution

Follow our step by step solution on how to calculate Friction Coefficient between Wheels and Road Surface using Retardation on Front Wheel?

FIRST Step Consider the formula

μ = a \cdot \frac{b}{[g] \cdot x \cdot \cos (θ) + a \cdot h}

Next Step Substitute values of Variables

∴

μ = 3.0191m/s² \cdot \frac{2.4m}{[g] \cdot 1.3m \cdot \cos (12°) + 3.0191m/s² \cdot 0.0075m}

Next Step Substitute values of Constants

∴

μ = 3.0191m/s² \cdot \frac{2.4m}{9.8066m/s² \cdot 1.3m \cdot \cos (12°) + 3.0191m/s² \cdot 0.0075m}

Next Step Convert Units

∴

μ = 3.0191m/s² \cdot \frac{2.4m}{9.8066m/s² \cdot 1.3m \cdot \cos (0.2094rad) + 3.0191m/s² \cdot 0.0075m}

Next Step Prepare to Evaluate

∴

μ = 3.0191 \cdot \frac{2.4}{9.8066 \cdot 1.3 \cdot \cos (0.2094) + 3.0191 \cdot 0.0075}

Next Step Evaluate

∴

μ = 0.579999989483687

LAST Step Rounding Answer

∴

μ = 0.58

Friction Coefficient between Wheels and Road Surface using Retardation on Front Wheel Formula Elements

Variables

Constants

Functions

Friction Coefficient Between Wheels And Ground BFW

Friction Coefficient Between Wheels And Ground BFW is the friction coefficient which is generated between wheels and ground when the brakes are applied.

Symbol: μ

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Friction Coefficient Between Wheels And Ground BFW

Braking Retardation BFW

Braking Retardation BFW is the negative acceleration of the vehicle which reduces its speed.

Symbol: a

Measurement: AccelerationUnit: m/s²

Note: Value can be positive or negative.

Formulas to find Braking Retardation BFW

Vehicle Wheelbase BFW

Vehicle Wheelbase BFW is the center distance between the front and the rear axle of the vehicle.

Symbol: b

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Vehicle Wheelbase BFW

Horizontal Distance of C.G. From Rear Axle BFW

Horizontal Distance of C.G. From Rear Axle BFW is the distance of vehicle's center of gravity (C.G.) form rear axle measured along wheelbase of vehicle.

Symbol: x

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Horizontal Distance of C.G. From Rear Axle BFW

Road Inclination Angle BFW

Road Inclination Angle BFW of Road is the angle which the road surface is making with the horizontal.

Symbol: θ

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Road Inclination Angle BFW

Height of C.G of Vehicle BFW

Height of C.G of Vehicle BFW is the theoretical point where the sum of all of the masses of each of its individual components effectively act.

Symbol: h

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Height of C.G of Vehicle BFW

Gravitational acceleration on Earth

Gravitational acceleration on Earth means that the velocity of an object in free fall will increase by 9.8 m/s2 every second.

Symbol: [g]

Value: 9.80665 m/s²

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: cos(Angle)

Other formulas in Effects due to Retardation category

Go Slope of Road using Retardation on Front Wheel

θ = a \cos (\frac{a}{[g] \cdot \frac{μ \cdot x}{b - μ \cdot h}})

Go Braking Retardation on Front Wheel

a = [g] \cdot \frac{μ \cdot x \cdot \cos (θ)}{b - μ \cdot h}

Go Horizontal Distance of C.G. from Rear Axle using Retardation on Front Wheel

x = \frac{a}{[g] \cdot \frac{μ \cdot \cos (θ)}{b - μ \cdot h}}

Go Vehicle Wheel Base using Retardation on Front Wheel

b = [g] \cdot \frac{μ \cdot x \cdot \cos (θ)}{a} + μ \cdot h

How to Evaluate Friction Coefficient between Wheels and Road Surface using Retardation on Front Wheel?

Friction Coefficient between Wheels and Road Surface using Retardation on Front Wheel evaluator uses Friction Coefficient Between Wheels And Ground BFW = Braking Retardation BFW*Vehicle Wheelbase BFW/([g]*Horizontal Distance of C.G. From Rear Axle BFW*cos(Road Inclination Angle BFW)+Braking Retardation BFW*Height of C.G of Vehicle BFW) to evaluate the Friction Coefficient Between Wheels And Ground BFW, Friction Coefficient between Wheels and Road Surface using Retardation on Front Wheel formula is used to find the measure of the amount of friction existing between ground and wheel. Friction Coefficient Between Wheels And Ground BFW is denoted by μ symbol.

How to evaluate Friction Coefficient between Wheels and Road Surface using Retardation on Front Wheel using this online evaluator? To use this online evaluator for Friction Coefficient between Wheels and Road Surface using Retardation on Front Wheel, enter Braking Retardation BFW (a), Vehicle Wheelbase BFW (b), Horizontal Distance of C.G. From Rear Axle BFW (x), Road Inclination Angle BFW (θ) & Height of C.G of Vehicle BFW (h) and hit the calculate button.

FAQs on Friction Coefficient between Wheels and Road Surface using Retardation on Front Wheel

What is the formula to find Friction Coefficient between Wheels and Road Surface using Retardation on Front Wheel?

The formula of Friction Coefficient between Wheels and Road Surface using Retardation on Front Wheel is expressed as Friction Coefficient Between Wheels And Ground BFW = Braking Retardation BFW*Vehicle Wheelbase BFW/([g]*Horizontal Distance of C.G. From Rear Axle BFW*cos(Road Inclination Angle BFW)+Braking Retardation BFW*Height of C.G of Vehicle BFW). Here is an example- 0.18853 = 3.019069*2.4/([g]*1.3*cos(0.20943951023928)+3.019069*0.0075).

How to calculate Friction Coefficient between Wheels and Road Surface using Retardation on Front Wheel?

With Braking Retardation BFW (a), Vehicle Wheelbase BFW (b), Horizontal Distance of C.G. From Rear Axle BFW (x), Road Inclination Angle BFW (θ) & Height of C.G of Vehicle BFW (h) we can find Friction Coefficient between Wheels and Road Surface using Retardation on Front Wheel using the formula - Friction Coefficient Between Wheels And Ground BFW = Braking Retardation BFW*Vehicle Wheelbase BFW/([g]*Horizontal Distance of C.G. From Rear Axle BFW*cos(Road Inclination Angle BFW)+Braking Retardation BFW*Height of C.G of Vehicle BFW). This formula also uses Gravitational acceleration on Earth constant(s) and Cosine function(s).

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Friction Coefficient between Wheels and Road Surface using Retardation on Front Wheel Formula

Friction Coefficient between Wheels and Road Surface using Retardation on Front Wheel Example

Friction Coefficient between Wheels and Road Surface using Retardation on Front Wheel Solution

Friction Coefficient between Wheels and Road Surface using Retardation on Front Wheel Formula Elements

Other formulas in Effects due to Retardation category

How to Evaluate Friction Coefficient between Wheels and Road Surface using Retardation on Front Wheel?

FAQs on Friction Coefficient between Wheels and Road Surface using Retardation on Front Wheel

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