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Tension in String given Coefficient of Friction of Inclined Plane Formula

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

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))

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

Tension in String given Coefficient of Friction of Inclined Plane Example

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Here is how the Tension in String given Coefficient of Friction of Inclined Plane equation looks like with Values.

Here is how the Tension in String given Coefficient of Friction of Inclined Plane equation looks like with Units.

Here is how the Tension in String given Coefficient of Friction of Inclined Plane equation looks like.

132.2499 = \frac{29 \cdot 13.52}{29 + 13.52} \cdot 9.8066 \cdot (1 + \sin (13.23) + 0.24 \cdot \cos (13.23))

132.2499N = \frac{29kg \cdot 13.52kg}{29kg + 13.52kg} \cdot 9.8066m/s² \cdot (1 + \sin (13.23°) + 0.24 \cdot \cos (13.23°))

132.2499 = \frac{29 \cdot 13.52}{29 + 13.52} \cdot 9.8066 \cdot (1 + \sin (13.23) + 0.24 \cdot \cos (13.23))

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Tension in String given Coefficient of Friction of Inclined Plane Solution

Follow our step by step solution on how to calculate Tension in String given Coefficient of Friction of Inclined Plane?

FIRST Step Consider the formula

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))

Next Step Substitute values of Variables

∴

T st = \frac{29kg \cdot 13.52kg}{29kg + 13.52kg} \cdot [g] \cdot (1 + \sin (13.23°) + 0.24 \cdot \cos (13.23°))

Next Step Substitute values of Constants

∴

T st = \frac{29kg \cdot 13.52kg}{29kg + 13.52kg} \cdot 9.8066m/s² \cdot (1 + \sin (13.23°) + 0.24 \cdot \cos (13.23°))

Next Step Convert Units

∴

T st = \frac{29kg \cdot 13.52kg}{29kg + 13.52kg} \cdot 9.8066m/s² \cdot (1 + \sin (0.2309rad) + 0.24 \cdot \cos (0.2309rad))

Next Step Prepare to Evaluate

∴

T st = \frac{29 \cdot 13.52}{29 + 13.52} \cdot 9.8066 \cdot (1 + \sin (0.2309) + 0.24 \cdot \cos (0.2309))

Next Step Evaluate

∴

T st = 132.249870605834N

LAST Step Rounding Answer

∴

T st = 132.2499N

Tension in String given Coefficient of Friction of Inclined Plane Formula Elements

Variables

Constants

Functions

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

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

Inclination of Plane

Inclination of Plane is the angle between the plane of motion and the horizontal when a body is hanging by a string.

Symbol: θ_p

Measurement: AngleUnit: °

Note: Value can be positive or negative.

Formulas to find Inclination of Plane

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

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

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.

Syntax: sin(Angle)

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: cos(Angle)

Other formulas in Body Lying on Rough Inclined Plane category

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 Coefficient of Friction given Tension

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)

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 Tension in String given Coefficient of Friction of Inclined Plane?

Tension in String given Coefficient of Friction of Inclined Plane evaluator 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 evaluate 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 evaluate Tension in String given Coefficient of Friction of Inclined Plane using this online evaluator? To use this online evaluator 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.

FAQs on Tension in String given Coefficient of Friction of Inclined Plane

What is the formula to find Tension in String given Coefficient of Friction of Inclined Plane?

The formula of Tension in String given Coefficient of Friction of Inclined Plane is expressed as 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)). Here is an example- 132.2499 = (29*13.52)/(29+13.52)*[g]*(1+sin(0.230907060038806)+0.24*cos(0.230907060038806)).

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

With Mass of Left Body (m₁), Mass of Right Body (m₂), Inclination of Plane (θ_p) & Coefficient of Friction for Hanging String (μ_hs) we can find Tension in String given Coefficient of Friction of Inclined Plane using the 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)). This formula also uses Gravitational acceleration on Earth constant(s) and , Sine (sin), Cosine (cos) function(s).

Can the Tension in String given Coefficient of Friction of Inclined Plane be negative?

Yes, the Tension in String given Coefficient of Friction of Inclined Plane, measured in Force can be negative.

Which unit is used to measure Tension in String given Coefficient of Friction of Inclined Plane?

Tension in String given Coefficient of Friction of Inclined Plane is usually measured using the Newton[N] for Force. Exanewton[N], Meganewton[N], Kilonewton[N] are the few other units in which Tension in String given Coefficient of Friction of Inclined Plane can be measured.

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