Efficiency of Inclined Plane when Effort Applied Horizontally to Move Body Upward Solution

STEP 0: Pre-Calculation Summary
Formula Used
Efficiency of Inclined Plane = tan(Angle of Inclination of Plane to Horizontal)/tan(Angle of Inclination of Plane to Horizontal+Limiting Angle of Friction)
η = tan(αi)/tan(αi+Φ)
This formula uses 1 Functions, 3 Variables
Functions Used
tan - The tangent of an angle is a trigonometric ratio of the length of the side opposite an angle to the length of the side adjacent to an angle in a right triangle., tan(Angle)
Variables Used
Efficiency of Inclined Plane - Efficiency of inclined plane tells us what fraction of the input energy (kinetic energy) does useful work (lifting).
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.
Limiting Angle of Friction - (Measured in Radian) - The Limiting Angle of Friction is defined as the angle which the resultant reaction (R) makes with the normal reaction (RN).
STEP 1: Convert Input(s) to Base Unit
Angle of Inclination of Plane to Horizontal: 23 Degree --> 0.40142572795862 Radian (Check conversion here)
Limiting Angle of Friction: 2 Degree --> 0.03490658503988 Radian (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
η = tan(αi)/tan(αi+Φ) --> tan(0.40142572795862)/tan(0.40142572795862+0.03490658503988)
Evaluating ... ...
η = 0.910289180943524
STEP 3: Convert Result to Output's Unit
0.910289180943524 --> No Conversion Required
FINAL ANSWER
0.910289180943524 0.910289 <-- Efficiency of Inclined Plane
(Calculation completed in 00.004 seconds)

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National Institute Of Technology (NIT), Hamirpur
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21 Angle Friction Calculators

Effort Applied to Move Body Downward on Inclined Plane Considering Friction
Go Effort to Move Downwards Considering Friction = (Weight of Body*sin(Angle of Inclination of Plane to Horizontal-Limiting Angle of Friction))/sin(Angle of Effort-(Angle of Inclination of Plane to Horizontal-Limiting Angle of Friction))
Effort Applied to Move Body Upward on Inclined Plane Considering Friction
Go Effort to Move Upwards Considering Friction = (Weight of Body*sin(Angle of Inclination of Plane to Horizontal+Limiting Angle of Friction))/sin(Angle of Effort-(Angle of Inclination of Plane to Horizontal+Limiting Angle of Friction))
Efficiency of Inclined Plane when Effort Applied to Move Body Downward
Go Efficiency of Inclined Plane = (cot(Angle of Inclination of Plane to Horizontal)-cot(Angle of Effort))/(cot(Angle of Inclination of Plane to Horizontal-Limiting Angle of Friction)-cot(Angle of Effort))
Efficiency of Inclined Plane when Effort Applied to Move Body Upward
Go Efficiency of Inclined Plane = (cot(Angle of Inclination of Plane to Horizontal+Limiting Angle of Friction)-cot(Angle of Effort))/(cot(Angle of Inclination of Plane to Horizontal)-cot(Angle of Effort))
Efficiency of Inclined Plane when Effort Applied Parallel to Move Body Downward
Go Efficiency of Inclined Plane = sin(Angle of Inclination of Plane to Horizontal-Limiting Angle of Friction)/(sin(Angle of Inclination of Plane to Horizontal)*cos(Limiting Angle of Friction))
Efficiency of Inclined Plane when Effort Applied Parallel to Move Body Upward
Go Efficiency of Inclined Plane = (sin(Angle of Inclination of Plane to Horizontal)*cos(Limiting Angle of Friction))/sin(Angle of Inclination of Plane to Horizontal+Limiting Angle of Friction)
Effort Applied Parallel to Inclined Plane to Move Body Downward Considering Friction
Go Effort to Move Downwards Considering Friction = Weight of Body*(sin(Angle of Inclination of Plane to Horizontal)-Coefficient of Friction*cos(Angle of Inclination of Plane to Horizontal))
Effort Applied Parallel to Inclined Plane to Move Body Upward Considering Friction
Go Effort to Move Upwards Considering Friction = Weight of Body*(sin(Angle of Inclination of Plane to Horizontal)+Coefficient of Friction*cos(Angle of Inclination of Plane to Horizontal))
Effort Required to Move Body down Plane Neglecting Friction
Go Effort Required to Move Neglecting Friction = (Weight of Body*sin(Angle of Inclination of Plane to Horizontal))/sin(Angle of Effort-Angle of Inclination of Plane to Horizontal)
Effort Required to Move Body up Plane Neglecting Friction
Go Effort Required to Move Neglecting Friction = (Weight of Body*sin(Angle of Inclination of Plane to Horizontal))/sin(Angle of Effort-Angle of Inclination of Plane to Horizontal)
Efficiency of Inclined Plane when Effort Applied Horizontally to Move Body Downward
Go Efficiency of Inclined Plane = tan(Angle of Inclination of Plane to Horizontal-Limiting Angle of Friction)/tan(Angle of Inclination of Plane to Horizontal)
Efficiency of Inclined Plane when Effort Applied Horizontally to Move Body Upward
Go Efficiency of Inclined Plane = tan(Angle of Inclination of Plane to Horizontal)/tan(Angle of Inclination of Plane to Horizontal+Limiting Angle of Friction)
Effort Applied Perpendicular to Inclined Plane to Move Body Downward Considering Friction
Go Effort to Move Downwards Considering Friction = Weight of Body*tan(Angle of Inclination of Plane to Horizontal-Limiting Angle of Friction)
Effort Applied Perpendicular to Inclined Plane to Move Body Upward Considering Friction
Go Effort to Move Upwards Considering Friction = Weight of Body*tan(Angle of Inclination of Plane to Horizontal+Limiting Angle of Friction)
Frictional Force between Cylinder and Inclined Plane surface for Rolling without Slipping
Go Force of Friction = (Mass of Cylinder*Acceleration due to Gravity*sin(Angle of Inclination))/3
Effort Applied Perpendicular to Inclined Plane to Move Body along Inclination Neglecting Friction
Go Effort Required to Move Neglecting Friction = Weight of Body*tan(Angle of Inclination of Plane to Horizontal)
Effort Applied Parallel to Inclined Plane to Move Body Upward or Downward Neglecting Friction
Go Effort Required to Move Neglecting Friction = Weight of Body*sin(Angle of Inclination of Plane to Horizontal)
Limiting Angle of Friction
Go Limiting Angle of Friction = atan(Limit Force/Normal Reaction)
Angle of Repose
Go Angle of Repose = atan(Limiting Force/Normal Reaction)
Minimum Force Required to Slide Body on Rough Horizontal Plane
Go Minimum Effort = Weight of Body*sin(Angle of Effort)
Coefficient of Friction between Cylinder and Surface of Inclined Plane for Rolling without Slipping
Go Coefficient of Friction = (tan(Angle of Inclination))/3

Efficiency of Inclined Plane when Effort Applied Horizontally to Move Body Upward Formula

Efficiency of Inclined Plane = tan(Angle of Inclination of Plane to Horizontal)/tan(Angle of Inclination of Plane to Horizontal+Limiting Angle of Friction)
η = tan(αi)/tan(αi+Φ)

What is the efficiency of the ramp?

The efficiency of the ramp tells us what fraction of the input energy (kinetic energy) does useful work (lifting).

How to Calculate Efficiency of Inclined Plane when Effort Applied Horizontally to Move Body Upward?

Efficiency of Inclined Plane when Effort Applied Horizontally to Move Body Upward calculator uses Efficiency of Inclined Plane = tan(Angle of Inclination of Plane to Horizontal)/tan(Angle of Inclination of Plane to Horizontal+Limiting Angle of Friction) to calculate the Efficiency of Inclined Plane, Efficiency of inclined plane when effort applied horizontally to move body upward on inclined plane tells us what fraction of the input energy (kinetic energy) does useful work (lifting). Efficiency of Inclined Plane is denoted by η symbol.

How to calculate Efficiency of Inclined Plane when Effort Applied Horizontally to Move Body Upward using this online calculator? To use this online calculator for Efficiency of Inclined Plane when Effort Applied Horizontally to Move Body Upward, enter Angle of Inclination of Plane to Horizontal i) & Limiting Angle of Friction (Φ) and hit the calculate button. Here is how the Efficiency of Inclined Plane when Effort Applied Horizontally to Move Body Upward calculation can be explained with given input values -> 0.910289 = tan(0.40142572795862)/tan(0.40142572795862+0.03490658503988).

FAQ

What is Efficiency of Inclined Plane when Effort Applied Horizontally to Move Body Upward?
Efficiency of inclined plane when effort applied horizontally to move body upward on inclined plane tells us what fraction of the input energy (kinetic energy) does useful work (lifting) and is represented as η = tan(αi)/tan(αi+Φ) or Efficiency of Inclined Plane = tan(Angle of Inclination of Plane to Horizontal)/tan(Angle of Inclination of Plane to Horizontal+Limiting Angle of Friction). Angle of inclination of plane to horizontal is formed by the inclination of one plane to another; measured in degrees or radians & The Limiting Angle of Friction is defined as the angle which the resultant reaction (R) makes with the normal reaction (RN).
How to calculate Efficiency of Inclined Plane when Effort Applied Horizontally to Move Body Upward?
Efficiency of inclined plane when effort applied horizontally to move body upward on inclined plane tells us what fraction of the input energy (kinetic energy) does useful work (lifting) is calculated using Efficiency of Inclined Plane = tan(Angle of Inclination of Plane to Horizontal)/tan(Angle of Inclination of Plane to Horizontal+Limiting Angle of Friction). To calculate Efficiency of Inclined Plane when Effort Applied Horizontally to Move Body Upward, you need Angle of Inclination of Plane to Horizontal i) & Limiting Angle of Friction (Φ). With our tool, you need to enter the respective value for Angle of Inclination of Plane to Horizontal & Limiting Angle of Friction 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 Efficiency of Inclined Plane?
In this formula, Efficiency of Inclined Plane uses Angle of Inclination of Plane to Horizontal & Limiting Angle of Friction. We can use 5 other way(s) to calculate the same, which is/are as follows -
  • Efficiency of Inclined Plane = tan(Angle of Inclination of Plane to Horizontal-Limiting Angle of Friction)/tan(Angle of Inclination of Plane to Horizontal)
  • Efficiency of Inclined Plane = sin(Angle of Inclination of Plane to Horizontal-Limiting Angle of Friction)/(sin(Angle of Inclination of Plane to Horizontal)*cos(Limiting Angle of Friction))
  • Efficiency of Inclined Plane = (sin(Angle of Inclination of Plane to Horizontal)*cos(Limiting Angle of Friction))/sin(Angle of Inclination of Plane to Horizontal+Limiting Angle of Friction)
  • Efficiency of Inclined Plane = (cot(Angle of Inclination of Plane to Horizontal)-cot(Angle of Effort))/(cot(Angle of Inclination of Plane to Horizontal-Limiting Angle of Friction)-cot(Angle of Effort))
  • Efficiency of Inclined Plane = (cot(Angle of Inclination of Plane to Horizontal+Limiting Angle of Friction)-cot(Angle of Effort))/(cot(Angle of Inclination of Plane to Horizontal)-cot(Angle of Effort))
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