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Tension in String if Both Bodies are Lying on Smooth Inclined Planes Formula

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Tension of String is the force exerted by a string on an object, causing it to accelerate or decelerate in a connected system of bodies. Check FAQs

T = \frac{m a \cdot m b}{m a + m b} \cdot [g] \cdot (\sin (α 1) + \sin (α 2))

T - Tension of String?m_a - Mass of Body A?m_b - Mass of Body B?α₁ - Inclination of Plane 1?α₂ - Inclination of Plane 2?[g] - Gravitational acceleration on Earth?

Tension in String if Both Bodies are Lying on Smooth Inclined Planes Example

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Here is how the Tension in String if Both Bodies are Lying on Smooth Inclined Planes equation looks like with Values.

Here is how the Tension in String if Both Bodies are Lying on Smooth Inclined Planes equation looks like with Units.

Here is how the Tension in String if Both Bodies are Lying on Smooth Inclined Planes equation looks like.

14.4525 = \frac{29.1 \cdot 1.11}{29.1 + 1.11} \cdot 9.8066 \cdot (\sin (34) + \sin (55))

14.4525N = \frac{29.1kg \cdot 1.11kg}{29.1kg + 1.11kg} \cdot 9.8066m/s² \cdot (\sin (34°) + \sin (55°))

14.4525 = \frac{29.1 \cdot 1.11}{29.1 + 1.11} \cdot 9.8066 \cdot (\sin (34) + \sin (55))

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Tension in String if Both Bodies are Lying on Smooth Inclined Planes Solution

Follow our step by step solution on how to calculate Tension in String if Both Bodies are Lying on Smooth Inclined Planes?

FIRST Step Consider the formula

T = \frac{m a \cdot m b}{m a + m b} \cdot [g] \cdot (\sin (α 1) + \sin (α 2))

Next Step Substitute values of Variables

∴

T = \frac{29.1kg \cdot 1.11kg}{29.1kg + 1.11kg} \cdot [g] \cdot (\sin (34°) + \sin (55°))

Next Step Substitute values of Constants

∴

T = \frac{29.1kg \cdot 1.11kg}{29.1kg + 1.11kg} \cdot 9.8066m/s² \cdot (\sin (34°) + \sin (55°))

Next Step Convert Units

∴

T = \frac{29.1kg \cdot 1.11kg}{29.1kg + 1.11kg} \cdot 9.8066m/s² \cdot (\sin (0.5934rad) + \sin (0.9599rad))

Next Step Prepare to Evaluate

∴

T = \frac{29.1 \cdot 1.11}{29.1 + 1.11} \cdot 9.8066 \cdot (\sin (0.5934) + \sin (0.9599))

Next Step Evaluate

∴

T = 14.4525285770719N

LAST Step Rounding Answer

∴

T = 14.4525N

Tension in String if Both Bodies are Lying on Smooth Inclined Planes Formula Elements

Variables

Constants

Functions

Tension of String

Tension of String is the force exerted by a string on an object, causing it to accelerate or decelerate in a connected system of bodies.

Symbol: T

Measurement: ForceUnit: N

Note: Value can be positive or negative.

Formulas to find Tension of String

Mass of Body A

Mass of Body A is the amount of matter in an object, a measure of its resistance to changes in its motion.

Symbol: m_a

Measurement: WeightUnit: kg

Note: Value should be greater than 0.

Formulas to find Mass of Body A

Mass of Body B

Mass of Body B is the quantity of matter in an object connected to another body through a string or cord.

Symbol: m_b

Measurement: WeightUnit: kg

Note: Value should be greater than 0.

Formulas to find Mass of Body B

Inclination of Plane 1

Inclination of Plane 1 is the angle between the plane and the horizontal surface in a system of bodies connected by strings.

Symbol: α₁

Measurement: AngleUnit: °

Note: Value can be positive or negative.

Formulas to find Inclination of Plane 1

Inclination of Plane 2

Inclination of Plane 2 is the angle between the plane of motion of the second body and the horizontal plane in a connected system.

Symbol: α₂

Measurement: AngleUnit: °

Note: Value can be positive or negative.

Formulas to find Inclination of Plane 2

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 Connected by String and Lying on Smooth Inclined Planes

a mb = \frac{m a \cdot \sin (α a) - m b \cdot \sin (α b)}{m a + m b} \cdot [g]

Go Angle of Inclination of Plane with Body A

α a = a \sin (\frac{m a \cdot a mb + T}{m a \cdot [g]})

Go Angle of Inclination of Plane with Body B

α b = a \sin (\frac{T - m b \cdot a mb}{m b \cdot [g]})

How to Evaluate Tension in String if Both Bodies are Lying on Smooth Inclined Planes?

Tension in String if Both Bodies are Lying on Smooth Inclined Planes evaluator uses Tension of String = (Mass of Body A*Mass of Body B)/(Mass of Body A+Mass of Body B)*[g]*(sin(Inclination of Plane 1)+sin(Inclination of Plane 2)) to evaluate the Tension of String, Tension in String if Both Bodies are Lying on Smooth Inclined Planes formula is defined as the measure of the force exerted by the string on the two bodies lying on smooth inclined planes, which is influenced by the masses of the bodies and the angles of inclination of the planes. Tension of String is denoted by T symbol.

How to evaluate Tension in String if Both Bodies are Lying on Smooth Inclined Planes using this online evaluator? To use this online evaluator for Tension in String if Both Bodies are Lying on Smooth Inclined Planes, enter Mass of Body A (m_a), Mass of Body B (m_b), Inclination of Plane 1 (α₁) & Inclination of Plane 2 (α₂) and hit the calculate button.

FAQs on Tension in String if Both Bodies are Lying on Smooth Inclined Planes

What is the formula to find Tension in String if Both Bodies are Lying on Smooth Inclined Planes?

The formula of Tension in String if Both Bodies are Lying on Smooth Inclined Planes is expressed as Tension of String = (Mass of Body A*Mass of Body B)/(Mass of Body A+Mass of Body B)*[g]*(sin(Inclination of Plane 1)+sin(Inclination of Plane 2)). Here is an example- 14.45253 = (29.1*1.11)/(29.1+1.11)*[g]*(sin(0.59341194567796)+sin(0.959931088596701)).

How to calculate Tension in String if Both Bodies are Lying on Smooth Inclined Planes?

With Mass of Body A (m_a), Mass of Body B (m_b), Inclination of Plane 1 (α₁) & Inclination of Plane 2 (α₂) we can find Tension in String if Both Bodies are Lying on Smooth Inclined Planes using the formula - Tension of String = (Mass of Body A*Mass of Body B)/(Mass of Body A+Mass of Body B)*[g]*(sin(Inclination of Plane 1)+sin(Inclination of Plane 2)). This formula also uses Gravitational acceleration on Earth constant(s) and Sine (sin) function(s).

Can the Tension in String if Both Bodies are Lying on Smooth Inclined Planes be negative?

Yes, the Tension in String if Both Bodies are Lying on Smooth Inclined Planes, measured in Force can be negative.

Which unit is used to measure Tension in String if Both Bodies are Lying on Smooth Inclined Planes?

Tension in String if Both Bodies are Lying on Smooth Inclined Planes 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 if Both Bodies are Lying on Smooth Inclined Planes can be measured.

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Tension in String if Both Bodies are Lying on Smooth Inclined Planes Formula

Tension in String if Both Bodies are Lying on Smooth Inclined Planes Example

Tension in String if Both Bodies are Lying on Smooth Inclined Planes Solution

Tension in String if Both Bodies are Lying on Smooth Inclined Planes Formula Elements

Other formulas in Body Lying on Smooth Inclined Plane category

How to Evaluate Tension in String if Both Bodies are Lying on Smooth Inclined Planes?

FAQs on Tension in String if Both Bodies are Lying on Smooth Inclined Planes

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