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Tension in String when One Body is Lying on Smooth Inclined Plane Formula

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Tension is the force exerted by a string on an object, such as a body, when it is hanging or suspended from a fixed point. Check FAQs

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

T - Tension?m₁ - Mass of Left Body?m₂ - Mass of Right Body?θ_p - Inclination of Plane?[g] - Gravitational acceleration on Earth?

Tension in String when One Body is Lying on Smooth Inclined Plane Example

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Here is how the Tension in String when One Body is Lying on Smooth Inclined Plane equation looks like with Values.

Here is how the Tension in String when One Body is Lying on Smooth Inclined Plane equation looks like with Units.

Here is how the Tension in String when One Body is Lying on Smooth Inclined Plane equation looks like.

111.1232 = \frac{29 \cdot 13.52}{29 + 13.52} \cdot 9.8066 \cdot (1 + \sin (13.23))

111.1232N = \frac{29kg \cdot 13.52kg}{29kg + 13.52kg} \cdot 9.8066m/s² \cdot (1 + \sin (13.23°))

111.1232 = \frac{29 \cdot 13.52}{29 + 13.52} \cdot 9.8066 \cdot (1 + \sin (13.23))

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Tension in String when One Body is Lying on Smooth Inclined Plane Solution

Follow our step by step solution on how to calculate Tension in String when One Body is Lying on Smooth Inclined Plane?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

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

Next Step Substitute values of Constants

∴

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

Next Step Convert Units

∴

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

Next Step Prepare to Evaluate

∴

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

Next Step Evaluate

∴

T = 111.123197759186N

LAST Step Rounding Answer

∴

T = 111.1232N

Tension in String when One Body is Lying on Smooth Inclined Plane Formula Elements

Variables

Constants

Functions

Tension

Tension is the force exerted by a string on an object, such as a body, when it is hanging or suspended from a fixed point.

Symbol: T

Measurement: ForceUnit: N

Note: Value can be positive or negative.

Formulas to find Tension

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

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)

Other formulas in Body Lying on Smooth Inclined Plane category

Go Acceleration of System with Bodies One Hanging Free and Other Lying on Smooth Inclined Plane

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

Go Angle of Inclination given Tension

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

Go Angle of Inclination given Acceleration

θ p = a \sin (\frac{m 1 \cdot [g] - m 1 \cdot a s - m 2 \cdot a s}{m 2 \cdot [g]})

How to Evaluate Tension in String when One Body is Lying on Smooth Inclined Plane?

Tension in String when One Body is Lying on Smooth Inclined Plane evaluator uses Tension = (Mass of Left Body*Mass of Right Body)/(Mass of Left Body+Mass of Right Body)*[g]*(1+sin(Inclination of Plane)) to evaluate the Tension, Tension in String when One Body is Lying on Smooth Inclined Plane formula is defined as the force exerted by the string on the body when it is placed on a smooth inclined plane, which depends on the masses of the body and the string, the acceleration due to gravity, and the angle of inclination of the plane. Tension is denoted by T symbol.

How to evaluate Tension in String when One Body is Lying on Smooth Inclined Plane using this online evaluator? To use this online evaluator for Tension in String when One Body is Lying on Smooth Inclined Plane, enter Mass of Left Body (m₁), Mass of Right Body (m₂) & Inclination of Plane (θ_p) and hit the calculate button.

FAQs on Tension in String when One Body is Lying on Smooth Inclined Plane

What is the formula to find Tension in String when One Body is Lying on Smooth Inclined Plane?

The formula of Tension in String when One Body is Lying on Smooth Inclined Plane is expressed as Tension = (Mass of Left Body*Mass of Right Body)/(Mass of Left Body+Mass of Right Body)*[g]*(1+sin(Inclination of Plane)). Here is an example- 111.1232 = (29*13.52)/(29+13.52)*[g]*(1+sin(0.230907060038806)).

How to calculate Tension in String when One Body is Lying on Smooth Inclined Plane?

With Mass of Left Body (m₁), Mass of Right Body (m₂) & Inclination of Plane (θ_p) we can find Tension in String when One Body is Lying on Smooth Inclined Plane using the formula - Tension = (Mass of Left Body*Mass of Right Body)/(Mass of Left Body+Mass of Right Body)*[g]*(1+sin(Inclination of Plane)). This formula also uses Gravitational acceleration on Earth constant(s) and Sine function(s).

Can the Tension in String when One Body is Lying on Smooth Inclined Plane be negative?

Yes, the Tension in String when One Body is Lying on Smooth Inclined Plane, measured in Force can be negative.

Which unit is used to measure Tension in String when One Body is Lying on Smooth Inclined Plane?

Tension in String when One Body is Lying on Smooth 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 when One Body is Lying on Smooth Inclined Plane can be measured.

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