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

GoEfficiency of Inclined Plane when Effort Applied Horizontally to Move Body Downward Formula

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

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Efficiency of Inclined Plane tells us what fraction of the input energy (kinetic energy) does useful work (lifting). Check FAQs

η = \frac{\sin (α i - Φ)}{\sin (α i) \cdot \cos (Φ)}

η - Efficiency of Inclined Plane?α_i - Angle of Inclination of Plane to Horizontal?Φ - Limiting Angle of Friction?

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

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Here is how the Efficiency of Inclined Plane when Effort Applied Parallel to Move Body Downward equation looks like with Values.

Here is how the Efficiency of Inclined Plane when Effort Applied Parallel to Move Body Downward equation looks like with Units.

Here is how the Efficiency of Inclined Plane when Effort Applied Parallel to Move Body Downward equation looks like.

0.9177 = \frac{\sin (23 - 2)}{\sin (23) \cdot \cos (2)}

0.9177 = \frac{\sin (23° - 2°)}{\sin (23°) \cdot \cos (2°)}

0.9177 = \frac{\sin (23 - 2)}{\sin (23) \cdot \cos (2)}

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

Follow our step by step solution on how to calculate Efficiency of Inclined Plane when Effort Applied Parallel to Move Body Downward?

FIRST Step Consider the formula

η = \frac{\sin (α i - Φ)}{\sin (α i) \cdot \cos (Φ)}

Next Step Substitute values of Variables

∴

η = \frac{\sin (23° - 2°)}{\sin (23°) \cdot \cos (2°)}

Next Step Convert Units

∴

η = \frac{\sin (0.4014rad - 0.0349rad)}{\sin (0.4014rad) \cdot \cos (0.0349rad)}

Next Step Prepare to Evaluate

∴

η = \frac{\sin (0.4014 - 0.0349)}{\sin (0.4014) \cdot \cos (0.0349)}

Next Step Evaluate

∴

η = 0.917731822576478

LAST Step Rounding Answer

∴

η = 0.9177

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

Variables

Functions

Efficiency of Inclined Plane

Efficiency of Inclined Plane tells us what fraction of the input energy (kinetic energy) does useful work (lifting).

Symbol: η

Measurement: NAUnit: Unitless

Note: Value should be less than 1.

Formulas to find Efficiency of Inclined Plane

Angle of Inclination of Plane to Horizontal

Angle of Inclination of Plane to Horizontal is formed by the inclination of one plane to another measured in degrees or radians.

Symbol: α_i

Measurement: AngleUnit: °

Note: Value should be less than 90.

Formulas to find Angle of Inclination of Plane to Horizontal

Limiting Angle of Friction

The Limiting Angle of Friction is defined as the angle which the resultant reaction (R) makes with the normal reaction (RN).

Symbol: Φ

Measurement: AngleUnit: °

Note: Value should be less than 90.

Formulas to find Limiting Angle of Friction

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.

Syntax: sin(Angle)

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 to find Efficiency of Inclined Plane

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

η = \frac{\tan (α i - Φ)}{\tan (α i)}

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

η = \frac{\tan (α i)}{\tan (α i + Φ)}

Go Efficiency of Inclined Plane when Effort Applied Parallel to Move Body Upward

η = \frac{\sin (α i) \cdot \cos (Φ)}{\sin (α i + Φ)}

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

η = \frac{\cot (α i) - \cot (θ e)}{\cot (α i - Φ) - \cot (θ e)}

Other formulas in Angle Friction category

Go Angle of Repose

α r = a \tan (\frac{F lim}{R n})

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

μ = \frac{\tan (θ i)}{3}

Go Effort Applied Parallel to Inclined Plane to Move Body Downward Considering Friction

P d = W \cdot (\sin (α i) - μ \cdot \cos (α i))

Go Effort Applied Parallel to Inclined Plane to Move Body Upward Considering Friction

P u = W \cdot (\sin (α i) + μ \cdot \cos (α i))

How to Evaluate Efficiency of Inclined Plane when Effort Applied Parallel to Move Body Downward?

Efficiency of Inclined Plane when Effort Applied Parallel to Move Body Downward evaluator 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 evaluate 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 evaluate Efficiency of Inclined Plane when Effort Applied Parallel to Move Body Downward using this online evaluator? To use this online evaluator 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.

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

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

The formula of Efficiency of Inclined Plane when Effort Applied Parallel to Move Body Downward is expressed as 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)). Here is an example- 0.917732 = sin(0.40142572795862-0.03490658503988)/(sin(0.40142572795862)*cos(0.03490658503988)).

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

With Angle of Inclination of Plane to Horizontal (α_i) & Limiting Angle of Friction (Φ) we can find Efficiency of Inclined Plane when Effort Applied Parallel to Move Body Downward using the formula - 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)). This formula also uses Sine (sin), Cosine (cos) function(s).

What are the other ways to Calculate Efficiency of Inclined Plane?

Here are the different ways to Calculate Efficiency of Inclined Plane-

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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