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

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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. Check FAQs

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

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

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

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Here is how the Acceleration of System with Bodies One Hanging Free and Other Lying on Smooth Inclined Plane equation looks like with Units.

Here is how the Acceleration of System with Bodies One Hanging Free and Other Lying on Smooth Inclined Plane equation looks like.

5.9748 = \frac{29 - 13.52 \cdot \sin (13.23)}{29 + 13.52} \cdot 9.8066

5.9748m/s² = \frac{29kg - 13.52kg \cdot \sin (13.23°)}{29kg + 13.52kg} \cdot 9.8066m/s²

5.9748 = \frac{29 - 13.52 \cdot \sin (13.23)}{29 + 13.52} \cdot 9.8066

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

Follow our step by step solution on how to calculate Acceleration of System with Bodies One Hanging Free and Other Lying on Smooth Inclined Plane?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

a s = \frac{29kg - 13.52kg \cdot \sin (13.23°)}{29kg + 13.52kg} \cdot [g]

Next Step Substitute values of Constants

∴

a s = \frac{29kg - 13.52kg \cdot \sin (13.23°)}{29kg + 13.52kg} \cdot 9.8066m/s²

Next Step Convert Units

∴

a s = \frac{29kg - 13.52kg \cdot \sin (0.2309rad)}{29kg + 13.52kg} \cdot 9.8066m/s²

Next Step Prepare to Evaluate

∴

a s = \frac{29 - 13.52 \cdot \sin (0.2309)}{29 + 13.52} \cdot 9.8066

Next Step Evaluate

∴

a s = 5.97481559451083m/s²

LAST Step Rounding Answer

∴

a s = 5.9748m/s²

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

Variables

Constants

Functions

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

Acceleration of System with Bodies One Hanging Free and Other Lying on Smooth Inclined Plane evaluator uses Acceleration of Body = (Mass of Left Body-Mass of Right Body*sin(Inclination of Plane))/(Mass of Left Body+Mass of Right Body)*[g] to evaluate the Acceleration of Body, Acceleration of System with Bodies One Hanging Free and Other Lying on Smooth Inclined Plane formula is defined as the rate of change of velocity of an object in a system consisting of two bodies, one hanging freely and the other lying on a smooth inclined plane, under the influence of gravity. Acceleration of Body is denoted by a_s symbol.

How to evaluate Acceleration of System with Bodies One Hanging Free and Other Lying on Smooth Inclined Plane using this online evaluator? To use this online evaluator for Acceleration of System with Bodies One Hanging Free and Other 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 Acceleration of System with Bodies One Hanging Free and Other Lying on Smooth Inclined Plane

What is the formula to find Acceleration of System with Bodies One Hanging Free and Other Lying on Smooth Inclined Plane?

The formula of Acceleration of System with Bodies One Hanging Free and Other Lying on Smooth Inclined Plane is expressed as Acceleration of Body = (Mass of Left Body-Mass of Right Body*sin(Inclination of Plane))/(Mass of Left Body+Mass of Right Body)*[g]. Here is an example- 5.974816 = (29-13.52*sin(0.230907060038806))/(29+13.52)*[g].

How to calculate Acceleration of System with Bodies One Hanging Free and Other Lying on Smooth Inclined Plane?

With Mass of Left Body (m₁), Mass of Right Body (m₂) & Inclination of Plane (θ_p) we can find Acceleration of System with Bodies One Hanging Free and Other Lying on Smooth Inclined Plane using the formula - Acceleration of Body = (Mass of Left Body-Mass of Right Body*sin(Inclination of Plane))/(Mass of Left Body+Mass of Right Body)*[g]. This formula also uses Gravitational acceleration on Earth constant(s) and Sine (sin) function(s).

Can the Acceleration of System with Bodies One Hanging Free and Other Lying on Smooth Inclined Plane be negative?

Yes, the Acceleration of System with Bodies One Hanging Free and Other Lying on Smooth Inclined Plane, measured in Acceleration can be negative.

Which unit is used to measure Acceleration of System with Bodies One Hanging Free and Other Lying on Smooth Inclined Plane?

Acceleration of System with Bodies One Hanging Free and Other Lying on Smooth Inclined Plane is usually measured using the Meter per Square Second[m/s²] for Acceleration. Kilometer per Square Second[m/s²], Micrometer per Square Second[m/s²], Mile per Square Second[m/s²] are the few other units in which Acceleration of System with Bodies One Hanging Free and Other Lying on Smooth Inclined Plane can be measured.

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