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Coefficient of Friction given Tension Formula

GoCoefficient of Friction given Frictional Force Formula

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Coefficient of Friction for Hanging String is the measure of the frictional force that opposes the motion of a body hanging by a string. Check FAQs

μ hs = \frac{m 1 + m 2}{m 1 \cdot m 1 \cdot [g]} \cdot T st \cdot \sec (θ b) - \tan (θ b) - \sec (θ b)

μ_hs - Coefficient of Friction for Hanging String?m₁ - Mass of Left Body?m₂ - Mass of Right Body?T_st - Tension in String?θ_b - Inclination of body?[g] - Gravitational acceleration on Earth?

Coefficient of Friction given Tension Example

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Here is how the Coefficient of Friction given Tension equation looks like with Values.

Here is how the Coefficient of Friction given Tension equation looks like with Units.

Here is how the Coefficient of Friction given Tension equation looks like.

0.2461 = \frac{29 + 13.52}{29 \cdot 29 \cdot 9.8066} \cdot 130 \cdot \sec (327.5) - \tan (327.5) - \sec (327.5)

0.2461 = \frac{29kg + 13.52kg}{29kg \cdot 29kg \cdot 9.8066m/s²} \cdot 130N \cdot \sec (327.5°) - \tan (327.5°) - \sec (327.5°)

0.2461 = \frac{29 + 13.52}{29 \cdot 29 \cdot 9.8066} \cdot 130 \cdot \sec (327.5) - \tan (327.5) - \sec (327.5)

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Coefficient of Friction given Tension Solution

Follow our step by step solution on how to calculate Coefficient of Friction given Tension?

FIRST Step Consider the formula

μ hs = \frac{m 1 + m 2}{m 1 \cdot m 1 \cdot [g]} \cdot T st \cdot \sec (θ b) - \tan (θ b) - \sec (θ b)

Next Step Substitute values of Variables

∴

μ hs = \frac{29kg + 13.52kg}{29kg \cdot 29kg \cdot [g]} \cdot 130N \cdot \sec (327.5°) - \tan (327.5°) - \sec (327.5°)

Next Step Substitute values of Constants

∴

μ hs = \frac{29kg + 13.52kg}{29kg \cdot 29kg \cdot 9.8066m/s²} \cdot 130N \cdot \sec (327.5°) - \tan (327.5°) - \sec (327.5°)

Next Step Convert Units

∴

μ hs = \frac{29kg + 13.52kg}{29kg \cdot 29kg \cdot 9.8066m/s²} \cdot 130N \cdot \sec (5.716rad) - \tan (5.716rad) - \sec (5.716rad)

Next Step Prepare to Evaluate

∴

μ hs = \frac{29 + 13.52}{29 \cdot 29 \cdot 9.8066} \cdot 130 \cdot \sec (5.716) - \tan (5.716) - \sec (5.716)

Next Step Evaluate

∴

μ hs = 0.24605839884811

LAST Step Rounding Answer

∴

μ hs = 0.2461

Coefficient of Friction given Tension Formula Elements

Variables

Constants

Functions

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.

Symbol: μ_hs

Measurement: NAUnit: Unitless

Note: Value should be between 0 to 1.

Formulas to find Coefficient of Friction for Hanging String

Mass of Left Body

Mass of Left Body is the amount of matter in an object hanging from a string, which affects the motion of the system.

Symbol: m₁

Measurement: WeightUnit: kg

Note: Value should be greater than 0.

Formulas to find Mass of Left Body

Mass of Right Body

Mass of Right Body is the amount of matter in an object hanging from a string, which affects its motion and oscillations.

Symbol: m₂

Measurement: WeightUnit: kg

Note: Value should be greater than 0.

Formulas to find Mass of Right Body

Tension in String

Tension in String is the force exerted by the string on the hanging object, opposing its weight and keeping it suspended in the air.

Symbol: T_st

Measurement: ForceUnit: N

Note: Value can be positive or negative.

Formulas to find Tension in String

Inclination of body

Inclination of body is the angle at which a body hangs from a string, measured from the vertical, affecting its motion and oscillations.

Symbol: θ_b

Measurement: AngleUnit: °

Note: Value can be positive or negative.

Formulas to find Inclination of body

Gravitational acceleration on Earth

Gravitational acceleration on Earth means that the velocity of an object in free fall will increase by 9.8 m/s2 every second.

Symbol: [g]

Value: 9.80665 m/s²

tan

The tangent of an angle is a trigonometric ratio of the length of the side opposite an angle to the length of the side adjacent to an angle in a right triangle.

Syntax: tan(Angle)

sec

Secant is a trigonometric function that is defined ratio of the hypotenuse to the shorter side adjacent to an acute angle (in a right-angled triangle); the reciprocal of a cosine.

Syntax: sec(Angle)

Other Formulas to find Coefficient of Friction for Hanging String

Go Coefficient of Friction given Frictional Force

μ hs = \frac{F fri}{m 2 \cdot [g] \cdot \cos (θ p)}

Other formulas in Body Lying on Rough Inclined Plane category

Go Tension in String given Coefficient of Friction of Inclined Plane

T st = \frac{m 1 \cdot m 2}{m 1 + m 2} \cdot [g] \cdot (1 + \sin (θ p) + μ hs \cdot \cos (θ p))

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

a i = \frac{m 1 - m 2 \cdot \sin (θ p) - μ hs \cdot m 2 \cdot \cos (θ p)}{m 1 + m 2} \cdot [g]

Go Frictional Force

F fri = μ hs \cdot m 2 \cdot [g] \cdot \cos (θ p)

Go Mass of Body B given Frictional Force

m 2 = \frac{F fri}{μ hs \cdot [g] \cdot \cos (θ p)}

How to Evaluate Coefficient of Friction given Tension?

Coefficient of Friction given Tension evaluator uses 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) to evaluate the Coefficient of Friction for Hanging String, Coefficient of Friction given Tension formula is defined as a measure of the ratio of the frictional force between two surfaces in contact to the normal force pressing them together, characterizing the frictional properties of the surfaces in a specific situation. Coefficient of Friction for Hanging String is denoted by μ_hs symbol.

How to evaluate Coefficient of Friction given Tension using this online evaluator? To use this online evaluator for Coefficient of Friction given Tension, enter Mass of Left Body (m₁), Mass of Right Body (m₂), Tension in String (T_st) & Inclination of body (θ_b) and hit the calculate button.

FAQs on Coefficient of Friction given Tension

What is the formula to find Coefficient of Friction given Tension?

The formula of Coefficient of Friction given Tension is expressed as 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). Here is an example- 0.246058 = (29+13.52)/(29*29*[g])*130*sec(5.71595330028035)-tan(5.71595330028035)-sec(5.71595330028035).

How to calculate Coefficient of Friction given Tension?

With Mass of Left Body (m₁), Mass of Right Body (m₂), Tension in String (T_st) & Inclination of body (θ_b) we can find Coefficient of Friction given Tension using the formula - 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). This formula also uses Gravitational acceleration on Earth constant(s) and , Tangent (tan), Secant (sec) function(s).

What are the other ways to Calculate Coefficient of Friction for Hanging String?

Here are the different ways to Calculate Coefficient of Friction for Hanging String-

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

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