Efficiency of Inclined Plane when Effort Applied to Move Body Upward Calculator

✖Angle of Inclination of Plane to Horizontal is formed by the inclination of one plane to another measured in degrees or radians.ⓘ Angle of Inclination of Plane to Horizontal [α_i]			+10% -10%
✖The Limiting Angle of Friction is defined as the angle which the resultant reaction (R) makes with the normal reaction (RN).ⓘ Limiting Angle of Friction [Φ]			+10% -10%
✖Angle of Effort is the angle which the line of action of effort makes with the weight of the body W.ⓘ Angle of Effort [θ_e]			+10% -10%

✖Efficiency of Inclined Plane tells us what fraction of the input energy (kinetic energy) does useful work (lifting).ⓘ Efficiency of Inclined Plane when Effort Applied to Move Body Upward [η]

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

STEP 0: Pre-Calculation Summary

Formula Used

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))
η = (cot(α_i+Φ)-cot(θ_e))/(cot(α_i)-cot(θ_e))
This formula uses 1 Functions, 4 Variables

Functions Used

cot - Cotangent is a trigonometric function that is defined as the ratio of the adjacent side to the opposite side in a right triangle., cot(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).
Angle of Effort - (Measured in Radian) - Angle of Effort is the angle which the line of action of effort makes with the weight of the body W.

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)
Angle of Effort: 85 Degree --> 1.4835298641949 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

η = (cot(α_i+Φ)-cot(θ_e))/(cot(α_i)-cot(θ_e)) --> (cot(0.40142572795862+0.03490658503988)-cot(1.4835298641949))/(cot(0.40142572795862)-cot(1.4835298641949))

Evaluating ... ...

η = 0.906829118672584

STEP 3: Convert Result to Output's Unit

0.906829118672584 --> No Conversion Required

FINAL ANSWER

0.906829118672584 ≈ 0.906829 <-- Efficiency of Inclined Plane

(Calculation completed in 00.008 seconds)

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< Angle Friction Calculators

Efficiency of Inclined Plane when Effort Applied Horizontally to Move Body Downward

LaTeX 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

LaTeX 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)

Angle of Repose

LaTeX Go Angle of Repose = atan(Limiting Force/Normal Reaction)

Coefficient of Friction between Cylinder and Surface of Inclined Plane for Rolling without Slipping

LaTeX Go Coefficient of Friction = (tan(Angle of Inclination))/3

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

LaTeX Go

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 to Move Body Upward?

Efficiency of Inclined Plane when Effort Applied to Move Body Upward calculator uses 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)) to calculate the Efficiency of Inclined Plane, Efficiency of Inclined Plane when Effort Applied to Move Body Upward formula is defined as a measure of the effectiveness of an inclined plane in converting the effort applied to move a body upward into useful work, taking into account the angle of inclination and the frictional forces involved. Efficiency of Inclined Plane is denoted by η symbol.

How to calculate Efficiency of Inclined Plane when Effort Applied to Move Body Upward using this online calculator? To use this online calculator for Efficiency of Inclined Plane when Effort Applied to Move Body Upward, enter Angle of Inclination of Plane to Horizontal (α_i), Limiting Angle of Friction (Φ) & Angle of Effort (θ_e) and hit the calculate button. Here is how the Efficiency of Inclined Plane when Effort Applied to Move Body Upward calculation can be explained with given input values -> 0.906829 = (cot(0.40142572795862+0.03490658503988)-cot(1.4835298641949))/(cot(0.40142572795862)-cot(1.4835298641949)).

FAQ

What is Efficiency of Inclined Plane when Effort Applied to Move Body Upward?

Efficiency of Inclined Plane when Effort Applied to Move Body Upward formula is defined as a measure of the effectiveness of an inclined plane in converting the effort applied to move a body upward into useful work, taking into account the angle of inclination and the frictional forces involved and is represented as η = (cot(α_i+Φ)-cot(θ_e))/(cot(α_i)-cot(θ_e)) or 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)). 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) & Angle of Effort is the angle which the line of action of effort makes with the weight of the body W.

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

Efficiency of Inclined Plane when Effort Applied to Move Body Upward formula is defined as a measure of the effectiveness of an inclined plane in converting the effort applied to move a body upward into useful work, taking into account the angle of inclination and the frictional forces involved is calculated using 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)). To calculate Efficiency of Inclined Plane when Effort Applied to Move Body Upward, you need Angle of Inclination of Plane to Horizontal (α_i), Limiting Angle of Friction (Φ) & Angle of Effort (θ_e). With our tool, you need to enter the respective value for Angle of Inclination of Plane to Horizontal, Limiting Angle of Friction & Angle of Effort 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 & Angle of Effort. We can use 3 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 = tan(Angle of Inclination of Plane to Horizontal)/tan(Angle of Inclination of Plane to Horizontal+Limiting Angle of Friction)
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))

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