Efficiency of Inclined Plane when Effort Applied Parallel to Move Body Downward 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%

✖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 Parallel to Move Body Downward [η]

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Efficiency of Inclined Plane when Effort Applied Parallel to Move Body Downward Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
η = sin(α_i-Φ)/(sin(α_i)*cos(Φ))
This formula uses 2 Functions, 3 Variables

Functions Used

sin - Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse., sin(Angle)
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

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 = sin(α_i-Φ)/(sin(α_i)*cos(Φ)) --> sin(0.40142572795862-0.03490658503988)/(sin(0.40142572795862)*cos(0.03490658503988))

Evaluating ... ...

η = 0.917731822576478

STEP 3: Convert Result to Output's Unit

0.917731822576478 --> No Conversion Required

FINAL ANSWER

0.917731822576478 ≈ 0.917732 <-- Efficiency of Inclined Plane

(Calculation completed in 00.020 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 Parallel to Move Body Downward 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 Parallel to Move Body Downward?

Efficiency of Inclined Plane when Effort Applied Parallel to Move Body Downward calculator uses 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)) to calculate the Efficiency of Inclined Plane, Efficiency of Inclined Plane when Effort Applied Parallel to Move Body Downward formula is defined as a measure of the effectiveness of an inclined plane in converting the effort applied into useful work when the effort is applied parallel to the plane to move a body downward. Efficiency of Inclined Plane is denoted by η symbol.

How to calculate Efficiency of Inclined Plane when Effort Applied Parallel to Move Body Downward using this online calculator? To use this online calculator for Efficiency of Inclined Plane when Effort Applied Parallel to Move Body Downward, enter Angle of Inclination of Plane to Horizontal (α_i) & Limiting Angle of Friction (Φ) and hit the calculate button. Here is how the Efficiency of Inclined Plane when Effort Applied Parallel to Move Body Downward calculation can be explained with given input values -> 0.917732 = sin(0.40142572795862-0.03490658503988)/(sin(0.40142572795862)*cos(0.03490658503988)).

FAQ

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

Efficiency of Inclined Plane when Effort Applied Parallel to Move Body Downward formula is defined as a measure of the effectiveness of an inclined plane in converting the effort applied into useful work when the effort is applied parallel to the plane to move a body downward and is represented as η = sin(α_i-Φ)/(sin(α_i)*cos(Φ)) or 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)). 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 Parallel to Move Body Downward?

Efficiency of Inclined Plane when Effort Applied Parallel to Move Body Downward formula is defined as a measure of the effectiveness of an inclined plane in converting the effort applied into useful work when the effort is applied parallel to the plane to move a body downward is calculated using 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)). To calculate Efficiency of Inclined Plane when Effort Applied Parallel to Move Body Downward, you need Angle of Inclination of Plane to Horizontal (α_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 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)*cos(Limiting Angle of Friction))/sin(Angle of Inclination of Plane to Horizontal+Limiting Angle of Friction)

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