Normal Reaction on Rear Wheels on Inclined Plane when Brakes Applied to All Four Wheels Solution

STEP 0: Pre-Calculation Summary
Formula Used
Normal reaction between ground and rear wheel = Mass of vehicle*Acceleration due to Gravity*cos(Angle of Inclination)-(Mass of vehicle*Acceleration due to Gravity*cos(Angle of inclination of plane to horizontal)*(Coefficient of Friction for Brake*Height of C.G. of vehicle+Perpendicular distance of C.G))/(Distance between center of rear and front wheels)
RB = m*g*cos(θi)-(m*g*cos(αinclination)*(μbrake*h+x))/(L)
This formula uses 1 Functions, 9 Variables
Functions Used
cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)
Variables Used
Normal reaction between ground and rear wheel - (Measured in Newton) - The normal reaction between ground and rear wheel is forced acting perpendicular to two surfaces in contact with each other.
Mass of vehicle - (Measured in Kilogram) - Mass of vehicle is a quantitative measure of inertia, a fundamental property of all matter.
Acceleration due to Gravity - (Measured in Meter per Square Second) - Acceleration due to Gravity is acceleration gained by an object because of gravitational force.
Angle of Inclination - (Measured in Radian) - Angle of Inclination is formed by the inclination of one line to another; measured in degrees or radians.
Angle of inclination of plane to horizontal - (Measured in Radian) - Angle of inclination of plane to horizontal is formed by the inclination of one plane to another; measured in degrees or radians.
Coefficient of Friction for Brake - Coefficient of Friction for Brake is the ratio defining the force that resists the motion of one body in relation to another body in contact with it.
Height of C.G. of vehicle - (Measured in Meter) - The height of C.G. of vehicle above the road surface is a numerical measurement of how far apart objects or points are.
Perpendicular distance of C.G - (Measured in Meter) - The perpendicular distance of C.G from the rear axle is a numerical measurement of how far apart objects or points are.
Distance between center of rear and front wheels - (Measured in Meter) - Distance between center of rear and front wheels is a numerical measurement of how far apart objects or points are.
STEP 1: Convert Input(s) to Base Unit
Mass of vehicle: 55 Kilogram --> 55 Kilogram No Conversion Required
Acceleration due to Gravity: 9.8 Meter per Square Second --> 9.8 Meter per Square Second No Conversion Required
Angle of Inclination: 30 Degree --> 0.5235987755982 Radian (Check conversion here)
Angle of inclination of plane to horizontal: 60 Degree --> 1.0471975511964 Radian (Check conversion here)
Coefficient of Friction for Brake: 0.35 --> No Conversion Required
Height of C.G. of vehicle: 10 Meter --> 10 Meter No Conversion Required
Perpendicular distance of C.G: 8 Meter --> 8 Meter No Conversion Required
Distance between center of rear and front wheels: 12 Meter --> 12 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
RB = m*g*cos(θi)-(m*g*cos(αinclination)*(μbrake*h+x))/(L) --> 55*9.8*cos(0.5235987755982)-(55*9.8*cos(1.0471975511964)*(0.35*10+8))/(12)
Evaluating ... ...
RB = 208.516859306391
STEP 3: Convert Result to Output's Unit
208.516859306391 Newton --> No Conversion Required
FINAL ANSWER
208.516859306391 208.5169 Newton <-- Normal reaction between ground and rear wheel
(Calculation completed in 00.004 seconds)

Credits

Created by Anshika Arya
National Institute Of Technology (NIT), Hamirpur
Anshika Arya has created this Calculator and 2000+ more calculators!
Verified by Payal Priya
Birsa Institute of Technology (BIT), Sindri
Payal Priya has verified this Calculator and 1900+ more calculators!

12 Total Normal Reaction Calculators

Normal Reaction on Rear Wheels on Inclined Plane when Brake Applied to Front Wheels
Go Normal reaction between ground and rear wheel = Mass of vehicle*Acceleration due to Gravity*cos(Angle of inclination of plane to horizontal)-(Mass of vehicle*Acceleration due to Gravity*cos(Angle of inclination of plane to horizontal)*Perpendicular distance of C.G)/(Distance between center of rear and front wheels-Coefficient of Friction for Brake*Height of C.G. of vehicle)
Normal Reaction on Rear Wheels on Inclined Plane when Brakes Applied to All Four Wheels
Go Normal reaction between ground and rear wheel = Mass of vehicle*Acceleration due to Gravity*cos(Angle of Inclination)-(Mass of vehicle*Acceleration due to Gravity*cos(Angle of inclination of plane to horizontal)*(Coefficient of Friction for Brake*Height of C.G. of vehicle+Perpendicular distance of C.G))/(Distance between center of rear and front wheels)
Total Normal Reaction between Ground and Front Wheels when Brakes are Applied to Rear Wheels only
Go Normal reaction between ground and front wheel = (Mass of vehicle*Acceleration due to Gravity*cos(Angle of inclination of plane to horizontal)*(Perpendicular distance of C.G+Coefficient of Friction for Brake*Height of C.G. of vehicle))/(Distance between center of rear and front wheels+Coefficient of Friction for Brake*Height of C.G. of vehicle)
Total Normal Reaction between Ground and Rear Wheels when Brakes Applied to Rear Wheels only
Go Normal reaction between ground and rear wheel = (Mass of vehicle*Acceleration due to Gravity*cos(Angle of inclination of plane to horizontal)*(Distance between center of rear and front wheels-Perpendicular distance of C.G))/(Distance between center of rear and front wheels+Coefficient of Friction for Brake*Height of C.G. of vehicle)
Total Normal Reaction between Ground and Front Wheels for 0 Accln, Brakes Applied to Rear Wheels
Go Normal reaction between ground and front wheel = (Mass of vehicle*Acceleration due to Gravity*(Perpendicular distance of C.G+Coefficient of Friction for Brake*Height of C.G. of vehicle))/(Distance between center of rear and front wheels+Coefficient of Friction for Brake*Height of C.G. of vehicle)
Normal Reaction on Front Wheels on Inclined Plane when Brakes Applied to All Four Wheels
Go Normal reaction between ground and front wheel = (Mass of vehicle*Acceleration due to Gravity*cos(Angle of inclination of plane to horizontal)*(Coefficient of Friction for Brake*Height of C.G. of vehicle+Perpendicular distance of C.G))/(Distance between center of rear and front wheels)
Normal Reaction on Front Wheels on Inclined Plane when Brake Applied to Front Wheels
Go Normal reaction between ground and front wheel = (Mass of vehicle*Acceleration due to Gravity*cos(Angle of inclination of plane to horizontal)*Perpendicular distance of C.G)/(Distance between center of rear and front wheels-Coefficient of Friction for Brake*Height of C.G. of vehicle)
Normal Reaction on Rear Wheels when Brakes Applied to All Four Wheels
Go Normal reaction between ground and rear wheel = Mass of vehicle*Acceleration due to Gravity-(Mass of vehicle*Acceleration due to Gravity*(Coefficient of Friction for Brake*Height of C.G. of vehicle+Perpendicular distance of C.G))/(Distance between center of rear and front wheels)
Normal Reaction on Rear Wheels when Brakes Applied to Front Wheels
Go Normal reaction between ground and rear wheel = Mass of vehicle*Acceleration due to Gravity-(Mass of vehicle*Acceleration due to Gravity*Perpendicular distance of C.G)/(Distance between center of rear and front wheels-Coefficient of Friction for Brake*Height of C.G. of vehicle)
Total Normal Reaction between Ground and Rear Wheels for 0 Accln, Brakes Applied to Rear Wheels
Go Normal reaction between ground and rear wheel = (Mass of vehicle*Acceleration due to Gravity*(Distance between center of rear and front wheels-Perpendicular distance of C.G))/(Distance between center of rear and front wheels+Coefficient of Friction for Brake*Height of C.G. of vehicle)
Normal Reaction on Front Wheels when Brakes Applied to All Four Wheels
Go Normal reaction between ground and front wheel = (Mass of vehicle*Acceleration due to Gravity*(Coefficient of Friction for Brake*Height of C.G. of vehicle+Perpendicular distance of C.G))/(Distance between center of rear and front wheels)
Normal Reaction on Front Wheels when Brakes Applied to Front Wheels
Go Normal reaction between ground and front wheel = (Mass of vehicle*Acceleration due to Gravity*Perpendicular distance of C.G)/(Distance between center of rear and front wheels-Coefficient of Friction for Brake*Height of C.G. of vehicle)

Normal Reaction on Rear Wheels on Inclined Plane when Brakes Applied to All Four Wheels Formula

Normal reaction between ground and rear wheel = Mass of vehicle*Acceleration due to Gravity*cos(Angle of Inclination)-(Mass of vehicle*Acceleration due to Gravity*cos(Angle of inclination of plane to horizontal)*(Coefficient of Friction for Brake*Height of C.G. of vehicle+Perpendicular distance of C.G))/(Distance between center of rear and front wheels)
RB = m*g*cos(θi)-(m*g*cos(αinclination)*(μbrake*h+x))/(L)

What is the brake?

A brake is a mechanical device that inhibits motion by absorbing energy from a moving system. It is used for slowing or stopping a moving vehicle, wheel, axle, or to prevent its motion, most often accomplished by means of friction.

How to Calculate Normal Reaction on Rear Wheels on Inclined Plane when Brakes Applied to All Four Wheels?

Normal Reaction on Rear Wheels on Inclined Plane when Brakes Applied to All Four Wheels calculator uses Normal reaction between ground and rear wheel = Mass of vehicle*Acceleration due to Gravity*cos(Angle of Inclination)-(Mass of vehicle*Acceleration due to Gravity*cos(Angle of inclination of plane to horizontal)*(Coefficient of Friction for Brake*Height of C.G. of vehicle+Perpendicular distance of C.G))/(Distance between center of rear and front wheels) to calculate the Normal reaction between ground and rear wheel, The Normal Reaction on Rear Wheels on Inclined Plane when Brakes Applied to all Four Wheels formula is defined as a force acting perpendicular to two surfaces in contact with each other. Normal reaction between ground and rear wheel is denoted by RB symbol.

How to calculate Normal Reaction on Rear Wheels on Inclined Plane when Brakes Applied to All Four Wheels using this online calculator? To use this online calculator for Normal Reaction on Rear Wheels on Inclined Plane when Brakes Applied to All Four Wheels, enter Mass of vehicle (m), Acceleration due to Gravity (g), Angle of Inclination i), Angle of inclination of plane to horizontal inclination), Coefficient of Friction for Brake brake), Height of C.G. of vehicle (h), Perpendicular distance of C.G (x) & Distance between center of rear and front wheels (L) and hit the calculate button. Here is how the Normal Reaction on Rear Wheels on Inclined Plane when Brakes Applied to All Four Wheels calculation can be explained with given input values -> -256.116562 = 55*9.8*cos(0.5235987755982)-(55*9.8*cos(1.0471975511964)*(0.35*10+8))/(12).

FAQ

What is Normal Reaction on Rear Wheels on Inclined Plane when Brakes Applied to All Four Wheels?
The Normal Reaction on Rear Wheels on Inclined Plane when Brakes Applied to all Four Wheels formula is defined as a force acting perpendicular to two surfaces in contact with each other and is represented as RB = m*g*cos(θi)-(m*g*cos(αinclination)*(μbrake*h+x))/(L) or Normal reaction between ground and rear wheel = Mass of vehicle*Acceleration due to Gravity*cos(Angle of Inclination)-(Mass of vehicle*Acceleration due to Gravity*cos(Angle of inclination of plane to horizontal)*(Coefficient of Friction for Brake*Height of C.G. of vehicle+Perpendicular distance of C.G))/(Distance between center of rear and front wheels). Mass of vehicle is a quantitative measure of inertia, a fundamental property of all matter, Acceleration due to Gravity is acceleration gained by an object because of gravitational force, Angle of Inclination is formed by the inclination of one line to another; measured in degrees or radians, Angle of inclination of plane to horizontal is formed by the inclination of one plane to another; measured in degrees or radians, Coefficient of Friction for Brake is the ratio defining the force that resists the motion of one body in relation to another body in contact with it, The height of C.G. of vehicle above the road surface is a numerical measurement of how far apart objects or points are, The perpendicular distance of C.G from the rear axle is a numerical measurement of how far apart objects or points are & Distance between center of rear and front wheels is a numerical measurement of how far apart objects or points are.
How to calculate Normal Reaction on Rear Wheels on Inclined Plane when Brakes Applied to All Four Wheels?
The Normal Reaction on Rear Wheels on Inclined Plane when Brakes Applied to all Four Wheels formula is defined as a force acting perpendicular to two surfaces in contact with each other is calculated using Normal reaction between ground and rear wheel = Mass of vehicle*Acceleration due to Gravity*cos(Angle of Inclination)-(Mass of vehicle*Acceleration due to Gravity*cos(Angle of inclination of plane to horizontal)*(Coefficient of Friction for Brake*Height of C.G. of vehicle+Perpendicular distance of C.G))/(Distance between center of rear and front wheels). To calculate Normal Reaction on Rear Wheels on Inclined Plane when Brakes Applied to All Four Wheels, you need Mass of vehicle (m), Acceleration due to Gravity (g), Angle of Inclination i), Angle of inclination of plane to horizontal inclination), Coefficient of Friction for Brake brake), Height of C.G. of vehicle (h), Perpendicular distance of C.G (x) & Distance between center of rear and front wheels (L). With our tool, you need to enter the respective value for Mass of vehicle, Acceleration due to Gravity, Angle of Inclination, Angle of inclination of plane to horizontal, Coefficient of Friction for Brake, Height of C.G. of vehicle, Perpendicular distance of C.G & Distance between center of rear and front wheels and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Normal reaction between ground and rear wheel?
In this formula, Normal reaction between ground and rear wheel uses Mass of vehicle, Acceleration due to Gravity, Angle of Inclination, Angle of inclination of plane to horizontal, Coefficient of Friction for Brake, Height of C.G. of vehicle, Perpendicular distance of C.G & Distance between center of rear and front wheels. We can use 5 other way(s) to calculate the same, which is/are as follows -
  • Normal reaction between ground and rear wheel = Mass of vehicle*Acceleration due to Gravity-(Mass of vehicle*Acceleration due to Gravity*(Coefficient of Friction for Brake*Height of C.G. of vehicle+Perpendicular distance of C.G))/(Distance between center of rear and front wheels)
  • Normal reaction between ground and rear wheel = Mass of vehicle*Acceleration due to Gravity-(Mass of vehicle*Acceleration due to Gravity*Perpendicular distance of C.G)/(Distance between center of rear and front wheels-Coefficient of Friction for Brake*Height of C.G. of vehicle)
  • Normal reaction between ground and rear wheel = (Mass of vehicle*Acceleration due to Gravity*(Distance between center of rear and front wheels-Perpendicular distance of C.G))/(Distance between center of rear and front wheels+Coefficient of Friction for Brake*Height of C.G. of vehicle)
  • Normal reaction between ground and rear wheel = Mass of vehicle*Acceleration due to Gravity*cos(Angle of inclination of plane to horizontal)-(Mass of vehicle*Acceleration due to Gravity*cos(Angle of inclination of plane to horizontal)*Perpendicular distance of C.G)/(Distance between center of rear and front wheels-Coefficient of Friction for Brake*Height of C.G. of vehicle)
  • Normal reaction between ground and rear wheel = (Mass of vehicle*Acceleration due to Gravity*cos(Angle of inclination of plane to horizontal)*(Distance between center of rear and front wheels-Perpendicular distance of C.G))/(Distance between center of rear and front wheels+Coefficient of Friction for Brake*Height of C.G. of vehicle)
Let Others Know
Facebook
Twitter
Reddit
LinkedIn
Email
WhatsApp
Copied!