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Inclination of Plane for given Frictional Force 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 \cos (\frac{F fri}{μ hs \cdot m 2 \cdot [g]})

θ_p - Inclination of Plane?F_fri - Force of Friction?μ_hs - Coefficient of Friction for Hanging String?m₂ - Mass of Right Body?[g] - Gravitational acceleration on Earth?

Inclination of Plane for given Frictional Force Example

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Here is how the Inclination of Plane for given Frictional Force equation looks like with Values.

Here is how the Inclination of Plane for given Frictional Force equation looks like with Units.

Here is how the Inclination of Plane for given Frictional Force equation looks like.

13.23 = a \cos (\frac{30.9761}{0.24 \cdot 13.52 \cdot 9.8066})

13.23° = a \cos (\frac{30.9761N}{0.24 \cdot 13.52kg \cdot 9.8066m/s²})

13.23 = a \cos (\frac{30.9761}{0.24 \cdot 13.52 \cdot 9.8066})

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Inclination of Plane for given Frictional Force Solution

Follow our step by step solution on how to calculate Inclination of Plane for given Frictional Force?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

θ p = a \cos (\frac{30.9761N}{0.24 \cdot 13.52kg \cdot [g]})

Next Step Substitute values of Constants

∴

θ p = a \cos (\frac{30.9761N}{0.24 \cdot 13.52kg \cdot 9.8066m/s²})

Next Step Prepare to Evaluate

∴

θ p = a \cos (\frac{30.9761}{0.24 \cdot 13.52 \cdot 9.8066})

Next Step Evaluate

∴

θ p = 0.230907530886902rad

Next Step Convert to Output's Unit

∴

θ p = 13.2300269776087°

LAST Step Rounding Answer

∴

θ p = 13.23°

Inclination of Plane for given Frictional Force 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

Force of Friction

Force of Friction is the force that opposes motion between two surfaces in contact, acting along the surface, when a body hangs by a string.

Symbol: F_fri

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Force of Friction

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 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

cos

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

Syntax: cos(Angle)

acos

The inverse cosine function, is the inverse function of the cosine function. It is the function that takes a ratio as an input and returns the angle whose cosine is equal to that ratio.

Syntax: acos(Number)

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 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)

How to Evaluate Inclination of Plane for given Frictional Force?

Inclination of Plane for given Frictional Force evaluator uses Inclination of Plane = acos(Force of Friction/(Coefficient of Friction for Hanging String*Mass of Right Body*[g])) to evaluate the Inclination of Plane, Inclination of Plane for given Frictional Force formula is defined as the angle at which a plane is inclined to the horizontal when a frictional force is applied, and it is a critical parameter in understanding the dynamics of motion on inclined planes. Inclination of Plane is denoted by θ_p symbol.

How to evaluate Inclination of Plane for given Frictional Force using this online evaluator? To use this online evaluator for Inclination of Plane for given Frictional Force, enter Force of Friction (F_fri), Coefficient of Friction for Hanging String (μ_hs) & Mass of Right Body (m₂) and hit the calculate button.

FAQs on Inclination of Plane for given Frictional Force

What is the formula to find Inclination of Plane for given Frictional Force?

The formula of Inclination of Plane for given Frictional Force is expressed as Inclination of Plane = acos(Force of Friction/(Coefficient of Friction for Hanging String*Mass of Right Body*[g])). Here is an example- 758.0247 = acos(30.97607/(0.24*13.52*[g])).

How to calculate Inclination of Plane for given Frictional Force?

With Force of Friction (F_fri), Coefficient of Friction for Hanging String (μ_hs) & Mass of Right Body (m₂) we can find Inclination of Plane for given Frictional Force using the formula - Inclination of Plane = acos(Force of Friction/(Coefficient of Friction for Hanging String*Mass of Right Body*[g])). This formula also uses Gravitational acceleration on Earth constant(s) and , Cosine, Inverse Cosine function(s).

Can the Inclination of Plane for given Frictional Force be negative?

Yes, the Inclination of Plane for given Frictional Force, measured in Angle can be negative.

Which unit is used to measure Inclination of Plane for given Frictional Force?

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

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