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Mass of One Meter Length of V-Belt given Belt Tension in Loose Side Formula

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Mass of Meter Length of V Belt is the mass of 1-meter length of the belt simply mass per unit length of the belt. Check FAQs

m v = \frac{P 1 - (e^{μ \cdot \frac{α}{\sin (\frac{θ}{2})}}) \cdot P 2}{{v b}^{2} \cdot (1 - (e^{μ \cdot \frac{α}{\sin (\frac{θ}{2})}}))}

m_v - Mass of Meter Length of V Belt?P₁ - Belt Tension on Tight Side?μ - Coefficient of Friction for Belt Drive?α - Wrap Angle on Pulley?θ - V Belt Angle?P₂ - Belt Tension on Loose Side?v_b - Belt Velocity?

Mass of One Meter Length of V-Belt given Belt Tension in Loose Side Example

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Here is how the Mass of One Meter Length of V-Belt given Belt Tension in Loose Side equation looks like with Values.

Here is how the Mass of One Meter Length of V-Belt given Belt Tension in Loose Side equation looks like with Units.

Here is how the Mass of One Meter Length of V-Belt given Belt Tension in Loose Side equation looks like.

0.7596 = \frac{800 - (e^{0.35 \cdot \frac{160.2}{\sin (\frac{62}{2})}}) \cdot 550}{{25.81}^{2} \cdot (1 - (e^{0.35 \cdot \frac{160.2}{\sin (\frac{62}{2})}}))}

0.7596kg/m = \frac{800N - (e^{0.35 \cdot \frac{160.2°}{\sin (\frac{62°}{2})}}) \cdot 550N}{{25.81m/s}^{2} \cdot (1 - (e^{0.35 \cdot \frac{160.2°}{\sin (\frac{62°}{2})}}))}

0.7596 = \frac{800 - (e^{0.35 \cdot \frac{160.2}{\sin (\frac{62}{2})}}) \cdot 550}{{25.81}^{2} \cdot (1 - (e^{0.35 \cdot \frac{160.2}{\sin (\frac{62}{2})}}))}

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Mass of One Meter Length of V-Belt given Belt Tension in Loose Side Solution

Follow our step by step solution on how to calculate Mass of One Meter Length of V-Belt given Belt Tension in Loose Side?

FIRST Step Consider the formula

m v = \frac{P 1 - (e^{μ \cdot \frac{α}{\sin (\frac{θ}{2})}}) \cdot P 2}{{v b}^{2} \cdot (1 - (e^{μ \cdot \frac{α}{\sin (\frac{θ}{2})}}))}

Next Step Substitute values of Variables

∴

m v = \frac{800N - (e^{0.35 \cdot \frac{160.2°}{\sin (\frac{62°}{2})}}) \cdot 550N}{{25.81m/s}^{2} \cdot (1 - (e^{0.35 \cdot \frac{160.2°}{\sin (\frac{62°}{2})}}))}

Next Step Convert Units

∴

m v = \frac{800N - (e^{0.35 \cdot \frac{2.796rad}{\sin (\frac{1.0821rad}{2})}}) \cdot 550N}{{25.81m/s}^{2} \cdot (1 - (e^{0.35 \cdot \frac{2.796rad}{\sin (\frac{1.0821rad}{2})}}))}

Next Step Prepare to Evaluate

∴

m v = \frac{800 - (e^{0.35 \cdot \frac{2.796}{\sin (\frac{1.0821}{2})}}) \cdot 550}{{25.81}^{2} \cdot (1 - (e^{0.35 \cdot \frac{2.796}{\sin (\frac{1.0821}{2})}}))}

Next Step Evaluate

∴

m v = 0.759634166315538kg/m

LAST Step Rounding Answer

∴

m v = 0.7596kg/m

Mass of One Meter Length of V-Belt given Belt Tension in Loose Side Formula Elements

Variables

Functions

Mass of Meter Length of V Belt

Mass of Meter Length of V Belt is the mass of 1-meter length of the belt simply mass per unit length of the belt.

Symbol: m_v

Measurement: Linear Mass DensityUnit: kg/m

Note: Value should be greater than 0.

Formulas to find Mass of Meter Length of V Belt

Belt Tension on Tight Side

Belt Tension on Tight Side is defined as the belt's tension on the belt's tight side.

Symbol: P₁

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Belt Tension on Tight Side

Coefficient of Friction for Belt Drive

Coefficient of Friction for Belt Drive is the ratio defining the force that resists the motion of the belt over the pulley.

Symbol: μ

Measurement: NAUnit: Unitless

Note: Value should be between 0 to 1.

Formulas to find Coefficient of Friction for Belt Drive

Wrap Angle on Pulley

Wrap Angle on Pulley is the angle between the run-up and run-off of the belt on the pulley.

Symbol: α

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Wrap Angle on Pulley

V Belt Angle

V Belt Angle is defined as the angle included between the side faces of the V cross-section belt.

Symbol: θ

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find V Belt Angle

Belt Tension on Loose Side

Belt Tension on Loose Side is defined as the belt's tension on the belt's loose side.

Symbol: P₂

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Belt Tension on Loose Side

Belt Velocity

Belt Velocity is defined as the velocity of the belt used in a belt drive.

Symbol: v_b

Measurement: SpeedUnit: m/s

Note: Value should be greater than 0.

Formulas to find Belt Velocity

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)

Other formulas in V Belt Characteristics and Parameters category

Go Belt Tension in Loose Side of V-Belt

P 2 = \frac{P 1 - m v \cdot {v b}^{2}}{e^{μ} \cdot \frac{α}{\sin (\frac{θ}{2})}} + m v \cdot {v b}^{2}

Go Belt Tension in Tight Side of V-Belt

P 1 = (e^{μ} \cdot \frac{α}{\sin (\frac{θ}{2})}) \cdot (P 2 - m v \cdot {v b}^{2}) + m v \cdot {v b}^{2}

How to Evaluate Mass of One Meter Length of V-Belt given Belt Tension in Loose Side?

Mass of One Meter Length of V-Belt given Belt Tension in Loose Side evaluator uses Mass of Meter Length of V Belt = (Belt Tension on Tight Side-(e^(Coefficient of Friction for Belt Drive*Wrap Angle on Pulley/sin(V Belt Angle/2)))*Belt Tension on Loose Side)/(Belt Velocity^2*(1-(e^(Coefficient of Friction for Belt Drive*Wrap Angle on Pulley/sin(V Belt Angle/2))))) to evaluate the Mass of Meter Length of V Belt, The Mass of One Meter Length of V-Belt given Belt Tension in Loose Side formula is defined as a method to determine the mass of a V-belt per meter based on the tension in its loose side, influencing the design and efficiency of belt drives. Mass of Meter Length of V Belt is denoted by m_v symbol.

How to evaluate Mass of One Meter Length of V-Belt given Belt Tension in Loose Side using this online evaluator? To use this online evaluator for Mass of One Meter Length of V-Belt given Belt Tension in Loose Side, enter Belt Tension on Tight Side (P₁), Coefficient of Friction for Belt Drive (μ), Wrap Angle on Pulley (α), V Belt Angle (θ), Belt Tension on Loose Side (P₂) & Belt Velocity (v_b) and hit the calculate button.

FAQs on Mass of One Meter Length of V-Belt given Belt Tension in Loose Side

What is the formula to find Mass of One Meter Length of V-Belt given Belt Tension in Loose Side?

The formula of Mass of One Meter Length of V-Belt given Belt Tension in Loose Side is expressed as Mass of Meter Length of V Belt = (Belt Tension on Tight Side-(e^(Coefficient of Friction for Belt Drive*Wrap Angle on Pulley/sin(V Belt Angle/2)))*Belt Tension on Loose Side)/(Belt Velocity^2*(1-(e^(Coefficient of Friction for Belt Drive*Wrap Angle on Pulley/sin(V Belt Angle/2))))). Here is an example- 0.759634 = (800-(e^(0.35*2.79601746169439/sin(1.08210413623628/2)))*550)/(25.81^2*(1-(e^(0.35*2.79601746169439/sin(1.08210413623628/2))))).

How to calculate Mass of One Meter Length of V-Belt given Belt Tension in Loose Side?

With Belt Tension on Tight Side (P₁), Coefficient of Friction for Belt Drive (μ), Wrap Angle on Pulley (α), V Belt Angle (θ), Belt Tension on Loose Side (P₂) & Belt Velocity (v_b) we can find Mass of One Meter Length of V-Belt given Belt Tension in Loose Side using the formula - Mass of Meter Length of V Belt = (Belt Tension on Tight Side-(e^(Coefficient of Friction for Belt Drive*Wrap Angle on Pulley/sin(V Belt Angle/2)))*Belt Tension on Loose Side)/(Belt Velocity^2*(1-(e^(Coefficient of Friction for Belt Drive*Wrap Angle on Pulley/sin(V Belt Angle/2))))). This formula also uses Sine (sin) function(s).

Can the Mass of One Meter Length of V-Belt given Belt Tension in Loose Side be negative?

No, the Mass of One Meter Length of V-Belt given Belt Tension in Loose Side, measured in Linear Mass Density cannot be negative.

Which unit is used to measure Mass of One Meter Length of V-Belt given Belt Tension in Loose Side?

Mass of One Meter Length of V-Belt given Belt Tension in Loose Side is usually measured using the Kilogram per Meter[kg/m] for Linear Mass Density. Gram per Meter[kg/m] are the few other units in which Mass of One Meter Length of V-Belt given Belt Tension in Loose Side can be measured.

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Mass of One Meter Length of V-Belt given Belt Tension in Loose Side Formula

Mass of One Meter Length of V-Belt given Belt Tension in Loose Side Example

Mass of One Meter Length of V-Belt given Belt Tension in Loose Side Solution

Mass of One Meter Length of V-Belt given Belt Tension in Loose Side Formula Elements

Other formulas in V Belt Characteristics and Parameters category

How to Evaluate Mass of One Meter Length of V-Belt given Belt Tension in Loose Side?

FAQs on Mass of One Meter Length of V-Belt given Belt Tension in Loose Side

Variable Name