Tension in String given Coefficient of Friction of Inclined Plane Calculator

✖Mass of Left Body is the amount of matter in an object hanging from a string, which affects the motion of the system.ⓘ Mass of Left Body [m₁]			+10% -10%
✖Mass of Right Body is the amount of matter in an object hanging from a string, which affects its motion and oscillations.ⓘ Mass of Right Body [m₂]			+10% -10%
✖Inclination of Plane is the angle between the plane of motion and the horizontal when a body is hanging by a string.ⓘ Inclination of Plane [θ_p]			+10% -10%
✖Coefficient of Friction for Hanging String is the measure of the frictional force that opposes the motion of a body hanging by a string.ⓘ Coefficient of Friction for Hanging String [μ_hs]			+10% -10%

✖Tension in String is the force exerted by the string on the hanging object, opposing its weight and keeping it suspended in the air.ⓘ Tension in String given Coefficient of Friction of Inclined Plane [T_st]

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Tension in String given Coefficient of Friction of Inclined Plane Solution

STEP 0: Pre-Calculation Summary

Formula Used

Tension in String = (Mass of Left Body*Mass of Right Body)/(Mass of Left Body+Mass of Right Body)*[g]*(1+sin(Inclination of Plane)+Coefficient of Friction for Hanging String*cos(Inclination of Plane))
T_st = (m₁*m₂)/(m₁+m₂)*[g]*(1+sin(θ_p)+μ_hs*cos(θ_p))
This formula uses 1 Constants, 2 Functions, 5 Variables

Constants Used

[g] - Gravitational acceleration on Earth Value Taken As 9.80665

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

Tension in String - (Measured in Newton) - Tension in String is the force exerted by the string on the hanging object, opposing its weight and keeping it suspended in the air.
Mass of Left Body - (Measured in Kilogram) - Mass of Left Body is the amount of matter in an object hanging from a string, which affects the motion of the system.
Mass of Right Body - (Measured in Kilogram) - Mass of Right Body is the amount of matter in an object hanging from a string, which affects its motion and oscillations.
Inclination of Plane - (Measured in Radian) - Inclination of Plane is the angle between the plane of motion and the horizontal when a body is hanging by a string.
Coefficient of Friction for Hanging String - Coefficient of Friction for Hanging String is the measure of the frictional force that opposes the motion of a body hanging by a string.

STEP 1: Convert Input(s) to Base Unit

Mass of Left Body: 29 Kilogram --> 29 Kilogram No Conversion Required
Mass of Right Body: 13.52 Kilogram --> 13.52 Kilogram No Conversion Required
Inclination of Plane: 13.23 Degree --> 0.230907060038806 Radian (Check conversion here)
Coefficient of Friction for Hanging String: 0.24 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

T_st = (m₁*m₂)/(m₁+m₂)*[g]*(1+sin(θ_p)+μ_hs*cos(θ_p)) --> (29*13.52)/(29+13.52)*[g]*(1+sin(0.230907060038806)+0.24*cos(0.230907060038806))

Evaluating ... ...

T_st = 132.249870605834

STEP 3: Convert Result to Output's Unit

132.249870605834 Newton --> No Conversion Required

FINAL ANSWER

132.249870605834 ≈ 132.2499 Newton <-- Tension in String

(Calculation completed in 00.004 seconds)

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Created by Vinay Mishra

Indian Institute for Aeronautical Engineering and Information Technology (IIAEIT), Pune

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Amrita School of Engineering (ASE), Vallikavu

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< Body Lying on Rough Inclined Plane Calculators

Coefficient of Friction given Tension

LaTeX Go Coefficient of Friction for Hanging String = (Mass of Left Body+Mass of Right Body)/(Mass of Left Body*Mass of Left Body*[g])*Tension in String*sec(Inclination of body)-tan(Inclination of body)-sec(Inclination of body)

Acceleration of System with Bodies One Hanging Free, Other Lying on Rough Inclined Plane

LaTeX Go Acceleration of System in Inclined Plane = (Mass of Left Body-Mass of Right Body*sin(Inclination of Plane)-Coefficient of Friction for Hanging String*Mass of Right Body*cos(Inclination of Plane))/(Mass of Left Body+Mass of Right Body)*[g]

Tension in String given Coefficient of Friction of Inclined Plane

LaTeX Go Tension in String = (Mass of Left Body*Mass of Right Body)/(Mass of Left Body+Mass of Right Body)*[g]*(1+sin(Inclination of Plane)+Coefficient of Friction for Hanging String*cos(Inclination of Plane))

Frictional Force

LaTeX Go Force of Friction = Coefficient of Friction for Hanging String*Mass of Right Body*[g]*cos(Inclination of Plane)

Tension in String given Coefficient of Friction of Inclined Plane Formula

LaTeX Go

What is Kinetic Friction?

Kinetic friction (also known as dynamic, or sliding friction) force is the friction force developed during the motion.

How to Calculate Tension in String given Coefficient of Friction of Inclined Plane?

Tension in String given Coefficient of Friction of Inclined Plane calculator uses Tension in String = (Mass of Left Body*Mass of Right Body)/(Mass of Left Body+Mass of Right Body)*[g]*(1+sin(Inclination of Plane)+Coefficient of Friction for Hanging String*cos(Inclination of Plane)) to calculate the Tension in String, Tension in String given Coefficient of Friction of Inclined Plane formula is defined as the measure of the force exerted by a string on an object, taking into account the coefficient of friction of the inclined plane, the masses of the objects, and the angle of inclination, providing a comprehensive understanding of the string's tension in various scenarios. Tension in String is denoted by T_st symbol.

How to calculate Tension in String given Coefficient of Friction of Inclined Plane using this online calculator? To use this online calculator for Tension in String given Coefficient of Friction of Inclined Plane, enter Mass of Left Body (m₁), Mass of Right Body (m₂), Inclination of Plane (θ_p) & Coefficient of Friction for Hanging String (μ_hs) and hit the calculate button. Here is how the Tension in String given Coefficient of Friction of Inclined Plane calculation can be explained with given input values -> 132.2499 = (29*13.52)/(29+13.52)*[g]*(1+sin(0.230907060038806)+0.24*cos(0.230907060038806)).

FAQ

What is Tension in String given Coefficient of Friction of Inclined Plane?

Tension in String given Coefficient of Friction of Inclined Plane formula is defined as the measure of the force exerted by a string on an object, taking into account the coefficient of friction of the inclined plane, the masses of the objects, and the angle of inclination, providing a comprehensive understanding of the string's tension in various scenarios and is represented as T_st = (m₁*m₂)/(m₁+m₂)*[g]*(1+sin(θ_p)+μ_hs*cos(θ_p)) or Tension in String = (Mass of Left Body*Mass of Right Body)/(Mass of Left Body+Mass of Right Body)*[g]*(1+sin(Inclination of Plane)+Coefficient of Friction for Hanging String*cos(Inclination of Plane)). Mass of Left Body is the amount of matter in an object hanging from a string, which affects the motion of the system, Mass of Right Body is the amount of matter in an object hanging from a string, which affects its motion and oscillations, Inclination of Plane is the angle between the plane of motion and the horizontal when a body is hanging by a string & Coefficient of Friction for Hanging String is the measure of the frictional force that opposes the motion of a body hanging by a string.

How to calculate Tension in String given Coefficient of Friction of Inclined Plane?

Tension in String given Coefficient of Friction of Inclined Plane formula is defined as the measure of the force exerted by a string on an object, taking into account the coefficient of friction of the inclined plane, the masses of the objects, and the angle of inclination, providing a comprehensive understanding of the string's tension in various scenarios is calculated using Tension in String = (Mass of Left Body*Mass of Right Body)/(Mass of Left Body+Mass of Right Body)*[g]*(1+sin(Inclination of Plane)+Coefficient of Friction for Hanging String*cos(Inclination of Plane)). To calculate Tension in String given Coefficient of Friction of Inclined Plane, you need Mass of Left Body (m₁), Mass of Right Body (m₂), Inclination of Plane (θ_p) & Coefficient of Friction for Hanging String (μ_hs). With our tool, you need to enter the respective value for Mass of Left Body, Mass of Right Body, Inclination of Plane & Coefficient of Friction for Hanging String and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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