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Mass per unit length of belt Formula

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

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

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

Mass per unit length of belt Example

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Here is how the Mass per unit length of belt equation looks like with Values.

Here is how the Mass per unit length of belt equation looks like with Units.

Here is how the Mass per unit length of belt equation looks like.

0.5997 = \frac{800 - ((e^{0.35 \cdot 160.2}) \cdot 550)}{({25.81}^{2}) \cdot (1 - (e^{0.35 \cdot 160.2}))}

0.5997kg/m = \frac{800N - ((e^{0.35 \cdot 160.2°}) \cdot 550N)}{({25.81m/s}^{2}) \cdot (1 - (e^{0.35 \cdot 160.2°}))}

0.5997 = \frac{800 - ((e^{0.35 \cdot 160.2}) \cdot 550)}{({25.81}^{2}) \cdot (1 - (e^{0.35 \cdot 160.2}))}

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Mass per unit length of belt Solution

Follow our step by step solution on how to calculate Mass per unit length of belt?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

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

Next Step Convert Units

∴

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

Next Step Prepare to Evaluate

∴

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

Next Step Evaluate

∴

m = 0.599656954727705kg/m

LAST Step Rounding Answer

∴

m = 0.5997kg/m

Mass per unit length of belt Formula Elements

Variables

Mass of Meter Length of Belt

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

Symbol: m

Measurement: Linear Mass DensityUnit: kg/m

Note: Value should be greater than 0.

Formulas to find Mass of Meter Length of 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

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

Other formulas in Introduction of Belt Drives category

Go Wrap Angle for Small Pulley

α s = 3.14 - (2 \cdot (a \sin (\frac{D - d}{2 \cdot C})))

Go Center Distance from Small Pulley to Big Pulley given Wrap Angle of Small Pulley

C = \frac{D - d}{2 \cdot \sin (\frac{3.14 - α s}{2})}

Go Diameter of Small Pulley given Wrap Angle of Small Pulley

d = D - (2 \cdot C \cdot \sin (\frac{3.14 - α s}{2}))

Go Diameter of Big Pulley given Wrap Angle of Small Pulley

D = d + (2 \cdot C \cdot \sin (\frac{3.14 - α s}{2}))

How to Evaluate Mass per unit length of belt?

Mass per unit length of belt evaluator uses Mass of Meter Length of Belt = (Belt Tension on Tight Side-((e^(Coefficient of Friction for Belt Drive*Wrap Angle on Pulley))*Belt Tension on Loose Side))/((Belt Velocity^2)*(1-(e^(Coefficient of Friction for Belt Drive*Wrap Angle on Pulley)))) to evaluate the Mass of Meter Length of Belt, The Mass per unit length of belt formula is defined as the mass of the belt per one meter length. Mass of Meter Length of Belt is denoted by m symbol.

How to evaluate Mass per unit length of belt using this online evaluator? To use this online evaluator for Mass per unit length of belt, enter Belt Tension on Tight Side (P₁), Coefficient of Friction for Belt Drive (μ), Wrap Angle on Pulley (α), Belt Tension on Loose Side (P₂) & Belt Velocity (v_b) and hit the calculate button.

FAQs on Mass per unit length of belt

What is the formula to find Mass per unit length of belt?

The formula of Mass per unit length of belt is expressed as Mass of Meter Length of Belt = (Belt Tension on Tight Side-((e^(Coefficient of Friction for Belt Drive*Wrap Angle on Pulley))*Belt Tension on Loose Side))/((Belt Velocity^2)*(1-(e^(Coefficient of Friction for Belt Drive*Wrap Angle on Pulley)))). Here is an example- 0.599657 = (800-((e^(0.35*2.79601746169439))*550))/((25.81^2)*(1-(e^(0.35*2.79601746169439)))).

How to calculate Mass per unit length of belt?

With Belt Tension on Tight Side (P₁), Coefficient of Friction for Belt Drive (μ), Wrap Angle on Pulley (α), Belt Tension on Loose Side (P₂) & Belt Velocity (v_b) we can find Mass per unit length of belt using the formula - Mass of Meter Length of Belt = (Belt Tension on Tight Side-((e^(Coefficient of Friction for Belt Drive*Wrap Angle on Pulley))*Belt Tension on Loose Side))/((Belt Velocity^2)*(1-(e^(Coefficient of Friction for Belt Drive*Wrap Angle on Pulley)))).

Can the Mass per unit length of belt be negative?

No, the Mass per unit length of belt, measured in Linear Mass Density cannot be negative.

Which unit is used to measure Mass per unit length of belt?

Mass per unit length of belt 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 per unit length of belt can be measured.

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Mass per unit length of belt Formula

Mass per unit length of belt Example

Mass per unit length of belt Solution

Mass per unit length of belt Formula Elements

Other formulas in Introduction of Belt Drives category

How to Evaluate Mass per unit length of belt?

FAQs on Mass per unit length of belt

Variable Name