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Velocity of the Belt When Tension of the Belt in Tight Side is Given Solution

STEP 0: Pre-Calculation Summary
Formula Used
belt_velocity = sqrt((Belt Tension in Tight Side-(e^Coefficient of Friction*Angle of Wrap)*Belt Tension in loose Side)/(Mass of Meter Length of Belt*(1-(e^Coefficient of Friction*Angle of Wrap))))
v = sqrt((P1-(e^μ*θ)*P2)/(m*(1-(e^μ*θ))))
This formula uses 1 Constants, 1 Functions, 5 Variables
Constants Used
e - Napier's constant Value Taken As 2.71828182845904523536028747135266249
Functions Used
sqrt - Squre root function, sqrt(Number)
Variables Used
Belt Tension in Tight Side - Belt Tension in Tight Side is defined as the tension of the belt in the tight side of the belt. (Measured in Newton)
Coefficient of Friction- The Coefficient of Friction (μ) is the ratio defining the force that resists the motion of one body in relation to another body in contact with it. This ratio is dependent on material properties and most materials have a value between 0 and 1.
Angle of Wrap - Angle of Wrap is defined as the distance, expressed in degrees. (Measured in Radian)
Belt Tension in loose Side - Belt Tension in loose Side is defined as the tension of the belt in the loose side of the belt. (Measured in Newton)
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.
STEP 1: Convert Input(s) to Base Unit
Belt Tension in Tight Side: 100 Newton --> 100 Newton No Conversion Required
Coefficient of Friction: 0.2 --> No Conversion Required
Angle of Wrap: 100 Radian --> 100 Radian No Conversion Required
Belt Tension in loose Side: 50 Newton --> 50 Newton No Conversion Required
Mass of Meter Length of Belt: 10 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
v = sqrt((P1-(e^μ*θ)*P2)/(m*(1-(e^μ*θ)))) --> sqrt((100-(e^0.2*100)*50)/(10*(1-(e^0.2*100))))
Evaluating ... ...
v = 2.22681960104832
STEP 3: Convert Result to Output's Unit
2.22681960104832 Meter per Second --> No Conversion Required
FINAL ANSWER
2.22681960104832 Meter per Second <-- Belt Velocity
(Calculation completed in 00.013 seconds)

10+ Design of Belt Drives Calculators

Belt Tension in the Tight Side
belt_tension_in_tight_side = (e^Coefficient of Friction*Angle of Wrap)*(Belt Tension in loose Side-Mass of Meter Length of Belt*Belt Velocity^2)+Mass of Meter Length of Belt*Belt Velocity^2 Go
Length of the Belt
belt_length = 2*Center Distance+(pi*(Diameter of Big Pulley+Diameter of Small Pulley)/2)+((Diameter of Big Pulley-Diameter of Small Pulley)^2/4*Center Distance) Go
Center Distance from Small Pulley to Big Pulley When Wrap Angle of Small Pulley is Given
center_distance = (Diameter of Big Pulley-Diameter of Small Pulley)/(2*sin((3.14-Wrap Angle for Small Pulley)/2)) Go
Center Distance from Small Pulley to Big Pulley When Wrap Angle of Big Pulley is Given
center_distance = (Diameter of Big Pulley-Diameter of Small Pulley)/(2*sin((Wrap Angle for Small Pulley-3.14)/2)) Go
Wrap Angle for the Small Pulley
wrap_angle_for_small_pulley = 3.14-2*asin((Diameter of Big Pulley-Diameter of Small Pulley)/2*Center Distance) Go
Diameter of Small Pully When Wrap Angle of the Big Pulley is Given
diameter_of_small_pulley = Diameter of Big Pulley-2*Center Distance*sin((Wrap Angle for Small Pulley-3.14)/2) Go
Diameter of Big Pulley When Wrap Angle for the Big Pulley is Given
diameter_of_big_pulley = Diameter of Small Pulley+2*Center Distance*sin((Wrap Angle for Small Pulley-3.14)/2) Go
Diameter of Small Pulley When Wrap Angle of Small Pulley is Given
diameter_of_small_pulley = Diameter of Big Pulley-2*Center Distance*sin((3.14-Wrap Angle for Small Pulley)/2) Go
Diameter of Big Pulley When Wrap Angle of Small Pulley is Given
diameter_of_big_pulley = Diameter of Small Pulley+2*Center Distance*sin((3.14-Wrap Angle for Small Pulley)/2) Go
Wrap Angle for the Big Pulley
wrap_angle_for_big_pulley = 3.14+2*asin((Diameter of Big Pulley-Diameter of Small Pulley)/2*Center Distance) Go

Velocity of the Belt When Tension of the Belt in Tight Side is Given Formula

belt_velocity = sqrt((Belt Tension in Tight Side-(e^Coefficient of Friction*Angle of Wrap)*Belt Tension in loose Side)/(Mass of Meter Length of Belt*(1-(e^Coefficient of Friction*Angle of Wrap))))
v = sqrt((P1-(e^μ*θ)*P2)/(m*(1-(e^μ*θ))))

Types of Belt Drives?

There are five different kinds of belt drive that can be found and those are: Open belt drive. Closed or crossed belt drive. Fast and loose cone pulley. Stepped cone pulley. Jockey pulley drive.

How to Calculate Velocity of the Belt When Tension of the Belt in Tight Side is Given?

Velocity of the Belt When Tension of the Belt in Tight Side is Given calculator uses belt_velocity = sqrt((Belt Tension in Tight Side-(e^Coefficient of Friction*Angle of Wrap)*Belt Tension in loose Side)/(Mass of Meter Length of Belt*(1-(e^Coefficient of Friction*Angle of Wrap)))) to calculate the Belt Velocity, The Velocity of the Belt When Tension of the Belt in Tight Side is Given is a measure of the rotational speed of the belt at which the rotational force is being transferred from one pulley to another. Belt Velocity and is denoted by v symbol.

How to calculate Velocity of the Belt When Tension of the Belt in Tight Side is Given using this online calculator? To use this online calculator for Velocity of the Belt When Tension of the Belt in Tight Side is Given, enter Belt Tension in Tight Side (P1), Coefficient of Friction (μ), Angle of Wrap (θ), Belt Tension in loose Side (P2) and Mass of Meter Length of Belt (m) and hit the calculate button. Here is how the Velocity of the Belt When Tension of the Belt in Tight Side is Given calculation can be explained with given input values -> 2.22682 = sqrt((100-(e^0.2*100)*50)/(10*(1-(e^0.2*100)))).

FAQ

What is Velocity of the Belt When Tension of the Belt in Tight Side is Given?
The Velocity of the Belt When Tension of the Belt in Tight Side is Given is a measure of the rotational speed of the belt at which the rotational force is being transferred from one pulley to another and is represented as v = sqrt((P1-(e^μ*θ)*P2)/(m*(1-(e^μ*θ)))) or belt_velocity = sqrt((Belt Tension in Tight Side-(e^Coefficient of Friction*Angle of Wrap)*Belt Tension in loose Side)/(Mass of Meter Length of Belt*(1-(e^Coefficient of Friction*Angle of Wrap)))). Belt Tension in Tight Side is defined as the tension of the belt in the tight side of the belt, The Coefficient of Friction (μ) is the ratio defining the force that resists the motion of one body in relation to another body in contact with it. This ratio is dependent on material properties and most materials have a value between 0 and 1. , Angle of Wrap is defined as the distance, expressed in degrees, Belt Tension in loose Side is defined as the tension of the belt in the loose side of the belt and Mass of Meter Length of Belt is the mass of 1-meter length of the belt simply mass per unit length of the belt.
How to calculate Velocity of the Belt When Tension of the Belt in Tight Side is Given?
The Velocity of the Belt When Tension of the Belt in Tight Side is Given is a measure of the rotational speed of the belt at which the rotational force is being transferred from one pulley to another is calculated using belt_velocity = sqrt((Belt Tension in Tight Side-(e^Coefficient of Friction*Angle of Wrap)*Belt Tension in loose Side)/(Mass of Meter Length of Belt*(1-(e^Coefficient of Friction*Angle of Wrap)))). To calculate Velocity of the Belt When Tension of the Belt in Tight Side is Given, you need Belt Tension in Tight Side (P1), Coefficient of Friction (μ), Angle of Wrap (θ), Belt Tension in loose Side (P2) and Mass of Meter Length of Belt (m). With our tool, you need to enter the respective value for Belt Tension in Tight Side, Coefficient of Friction, Angle of Wrap, Belt Tension in loose Side and Mass of Meter Length of Belt 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 Belt Velocity?
In this formula, Belt Velocity uses Belt Tension in Tight Side, Coefficient of Friction, Angle of Wrap, Belt Tension in loose Side and Mass of Meter Length of Belt. We can use 10 other way(s) to calculate the same, which is/are as follows -
  • wrap_angle_for_small_pulley = 3.14-2*asin((Diameter of Big Pulley-Diameter of Small Pulley)/2*Center Distance)
  • center_distance = (Diameter of Big Pulley-Diameter of Small Pulley)/(2*sin((3.14-Wrap Angle for Small Pulley)/2))
  • diameter_of_small_pulley = Diameter of Big Pulley-2*Center Distance*sin((3.14-Wrap Angle for Small Pulley)/2)
  • diameter_of_big_pulley = Diameter of Small Pulley+2*Center Distance*sin((3.14-Wrap Angle for Small Pulley)/2)
  • wrap_angle_for_big_pulley = 3.14+2*asin((Diameter of Big Pulley-Diameter of Small Pulley)/2*Center Distance)
  • center_distance = (Diameter of Big Pulley-Diameter of Small Pulley)/(2*sin((Wrap Angle for Small Pulley-3.14)/2))
  • diameter_of_small_pulley = Diameter of Big Pulley-2*Center Distance*sin((Wrap Angle for Small Pulley-3.14)/2)
  • diameter_of_big_pulley = Diameter of Small Pulley+2*Center Distance*sin((Wrap Angle for Small Pulley-3.14)/2)
  • belt_length = 2*Center Distance+(pi*(Diameter of Big Pulley+Diameter of Small Pulley)/2)+((Diameter of Big Pulley-Diameter of Small Pulley)^2/4*Center Distance)
  • belt_tension_in_tight_side = (e^Coefficient of Friction*Angle of Wrap)*(Belt Tension in loose Side-Mass of Meter Length of Belt*Belt Velocity^2)+Mass of Meter Length of Belt*Belt Velocity^2
Where is the Velocity of the Belt When Tension of the Belt in Tight Side is Given calculator used?
Among many, Velocity of the Belt When Tension of the Belt in Tight Side is Given calculator is widely used in real life applications like {FormulaUses}. Here are few more real life examples -
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