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Angle of Inclination given Acceleration Formula

GoAngle of Inclination given Tension Formula

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

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

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

Angle of Inclination given Acceleration Example

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Here is how the Angle of Inclination given Acceleration equation looks like with Values.

Here is how the Angle of Inclination given Acceleration equation looks like with Units.

Here is how the Angle of Inclination given Acceleration equation looks like.

13.8881 = a \sin (\frac{29 \cdot 9.8066 - 29 \cdot 5.94 - 13.52 \cdot 5.94}{13.52 \cdot 9.8066})

13.8881° = a \sin (\frac{29kg \cdot 9.8066m/s² - 29kg \cdot 5.94m/s² - 13.52kg \cdot 5.94m/s²}{13.52kg \cdot 9.8066m/s²})

13.8881 = a \sin (\frac{29 \cdot 9.8066 - 29 \cdot 5.94 - 13.52 \cdot 5.94}{13.52 \cdot 9.8066})

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Angle of Inclination given Acceleration Solution

Follow our step by step solution on how to calculate Angle of Inclination given Acceleration?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

θ p = a \sin (\frac{29kg \cdot [g] - 29kg \cdot 5.94m/s² - 13.52kg \cdot 5.94m/s²}{13.52kg \cdot [g]})

Next Step Substitute values of Constants

∴

θ p = a \sin (\frac{29kg \cdot 9.8066m/s² - 29kg \cdot 5.94m/s² - 13.52kg \cdot 5.94m/s²}{13.52kg \cdot 9.8066m/s²})

Next Step Prepare to Evaluate

∴

θ p = a \sin (\frac{29 \cdot 9.8066 - 29 \cdot 5.94 - 13.52 \cdot 5.94}{13.52 \cdot 9.8066})

Next Step Evaluate

∴

θ p = 0.242392516176502rad

Next Step Convert to Output's Unit

∴

θ p = 13.8880681624727°

LAST Step Rounding Answer

∴

θ p = 13.8881°

Angle of Inclination given Acceleration Formula Elements

Variables

Constants

Functions

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

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

Acceleration of Body

Acceleration of Body is the rate of change of velocity of an object hanging by a string, describing its motion under the influence of gravity.

Symbol: a_s

Measurement: AccelerationUnit: m/s²

Note: Value can be positive or negative.

Formulas to find Acceleration of 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

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

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)

asin

The inverse sine function, is a trigonometric function that takes a ratio of two sides of a right triangle and outputs the angle opposite the side with the given ratio.

Syntax: asin(Number)

Other Formulas to find Inclination of Plane

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)

Other formulas in Body Lying on Smooth Inclined Plane category

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

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

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]

How to Evaluate Angle of Inclination given Acceleration?

Angle of Inclination given Acceleration evaluator uses Inclination of Plane = asin((Mass of Left Body*[g]-Mass of Left Body*Acceleration of Body-Mass of Right Body*Acceleration of Body)/(Mass of Right Body*[g])) to evaluate the Inclination of Plane, Angle of Inclination given Acceleration formula is defined as a measure of the angle at which an object is inclined from the horizontal, which affects the acceleration of the object due to gravity and other external forces, and is essential in understanding the motion of objects on inclined planes. Inclination of Plane is denoted by θ_p symbol.

How to evaluate Angle of Inclination given Acceleration using this online evaluator? To use this online evaluator for Angle of Inclination given Acceleration, enter Mass of Left Body (m₁), Acceleration of Body (a_s) & Mass of Right Body (m₂) and hit the calculate button.

FAQs on Angle of Inclination given Acceleration

What is the formula to find Angle of Inclination given Acceleration?

The formula of Angle of Inclination given Acceleration is expressed as Inclination of Plane = asin((Mass of Left Body*[g]-Mass of Left Body*Acceleration of Body-Mass of Right Body*Acceleration of Body)/(Mass of Right Body*[g])). Here is an example- 795.7277 = asin((29*[g]-29*5.94-13.52*5.94)/(13.52*[g])).

How to calculate Angle of Inclination given Acceleration?

With Mass of Left Body (m₁), Acceleration of Body (a_s) & Mass of Right Body (m₂) we can find Angle of Inclination given Acceleration using the formula - Inclination of Plane = asin((Mass of Left Body*[g]-Mass of Left Body*Acceleration of Body-Mass of Right Body*Acceleration of Body)/(Mass of Right Body*[g])). This formula also uses Gravitational acceleration on Earth, Gravitational acceleration on Earth constant(s) and , Sine (sin), Inverse Sine (asin) function(s).

What are the other ways to Calculate Inclination of Plane?

Here are the different ways to Calculate Inclination of Plane-

Inclination of Plane=asin((Tension*(Mass of Left Body+Mass of Right Body))/(Mass of Left Body*Mass of Right Body*[g])-1)

Can the Angle of Inclination given Acceleration be negative?

Yes, the Angle of Inclination given Acceleration, measured in Angle can be negative.

Which unit is used to measure Angle of Inclination given Acceleration?

Angle of Inclination given Acceleration is usually measured using the Degree[°] for Angle. Radian[°], Minute[°], Second[°] are the few other units in which Angle of Inclination given Acceleration can be measured.

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