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))
Tst = (m1*m2)/(m1+m2)*[g]*(1+sin(θp)+μhs*cos(θp))
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 described as the pulling force transmitted axially by the means of a string.
Mass of Left Body - (Measured in Kilogram) - Mass of Left Body is the measure of the quantity of matter that a body or an object contains.
Mass of Right Body - (Measured in Kilogram) - Mass of Right Body is the measure of the quantity of matter that a body or an object contains.
Inclination of Plane - (Measured in Radian) - The inclination of Plane is the angle a tilted ramp makes with the flat surface.
Coefficient of Friction for Hanging String - Coefficient of Friction for Hanging String is the ratio defining the force that resists the motion of one body in relation to another body in contact with it.
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
Tst = (m1*m2)/(m1+m2)*[g]*(1+sin(θp)+μhs*cos(θp)) --> (29*13.52)/(29+13.52)*[g]*(1+sin(0.230907060038806)+0.24*cos(0.230907060038806))
Evaluating ... ...
Tst = 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 00.020 seconds)

Credits

Created by Vinay Mishra
Indian Institute for Aeronautical Engineering and Information Technology (IIAEIT), Pune
Vinay Mishra has created this Calculator and 300+ more calculators!
Verified by Sanjay Krishna
Amrita School of Engineering (ASE), Vallikavu
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7 Body Lying on Rough Inclined Plane Calculators

Coefficient of Friction given Tension
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
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
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))
Coefficient of Friction given Frictional Force
Go Coefficient of Friction for Hanging String = Force of Friction/(Mass of Right Body*[g]*cos(Inclination of Plane))
Inclination of Plane for given Frictional Force
Go Inclination of Plane = acos(Force of Friction/(Coefficient of Friction for Hanging String*Mass of Right Body*[g]))
Mass of Body B given Frictional Force
Go Mass of Right Body = Force of Friction/(Coefficient of Friction for Hanging String*[g]*cos(Inclination of Plane))
Frictional Force
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

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))
Tst = (m1*m2)/(m1+m2)*[g]*(1+sin(θp)+μhs*cos(θp))

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, The Tension in string given coefficient of friction of inclined plane, is the function of the masses of both bodies, coefficient of friction between surfaces and the angle of inclination of the plane. Tension in String is denoted by Tst 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 p) & Coefficient of Friction for Hanging String 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?
The Tension in string given coefficient of friction of inclined plane, is the function of the masses of both bodies, coefficient of friction between surfaces and the angle of inclination of the plane and is represented as Tst = (m1*m2)/(m1+m2)*[g]*(1+sin(θp)+μhs*cos(θp)) 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 measure of the quantity of matter that a body or an object contains, Mass of Right Body is the measure of the quantity of matter that a body or an object contains, The inclination of Plane is the angle a tilted ramp makes with the flat surface & Coefficient of Friction for Hanging String is the ratio defining the force that resists the motion of one body in relation to another body in contact with it.
How to calculate Tension in String given Coefficient of Friction of Inclined Plane?
The Tension in string given coefficient of friction of inclined plane, is the function of the masses of both bodies, coefficient of friction between surfaces and the angle of inclination of the plane 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 p) & Coefficient of Friction for Hanging String 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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