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Acceleration of System with Bodies One Hanging Free, Other Lying on Rough Inclined Plane Formula

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Acceleration of System in Inclined Plane is the rate of change of velocity of an object hanging by a string on an inclined plane. Check FAQs

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]

a_i - Acceleration of System in Inclined Plane?m₁ - Mass of Left Body?m₂ - Mass of Right Body?θ_p - Inclination of Plane?μ_hs - Coefficient of Friction for Hanging String?[g] - Gravitational acceleration on Earth?

Acceleration of System with Bodies One Hanging Free, Other Lying on Rough Inclined Plane Example

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

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

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

5.2463 = \frac{29 - 13.52 \cdot \sin (13.23) - 0.24 \cdot 13.52 \cdot \cos (13.23)}{29 + 13.52} \cdot 9.8066

5.2463m/s² = \frac{29kg - 13.52kg \cdot \sin (13.23°) - 0.24 \cdot 13.52kg \cdot \cos (13.23°)}{29kg + 13.52kg} \cdot 9.8066m/s²

5.2463 = \frac{29 - 13.52 \cdot \sin (13.23) - 0.24 \cdot 13.52 \cdot \cos (13.23)}{29 + 13.52} \cdot 9.8066

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Acceleration of System with Bodies One Hanging Free, Other Lying on Rough Inclined Plane Solution

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

FIRST Step Consider the formula

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]

Next Step Substitute values of Variables

∴

a i = \frac{29kg - 13.52kg \cdot \sin (13.23°) - 0.24 \cdot 13.52kg \cdot \cos (13.23°)}{29kg + 13.52kg} \cdot [g]

Next Step Substitute values of Constants

∴

a i = \frac{29kg - 13.52kg \cdot \sin (13.23°) - 0.24 \cdot 13.52kg \cdot \cos (13.23°)}{29kg + 13.52kg} \cdot 9.8066m/s²

Next Step Convert Units

∴

a i = \frac{29kg - 13.52kg \cdot \sin (0.2309rad) - 0.24 \cdot 13.52kg \cdot \cos (0.2309rad)}{29kg + 13.52kg} \cdot 9.8066m/s²

Next Step Prepare to Evaluate

∴

a i = \frac{29 - 13.52 \cdot \sin (0.2309) - 0.24 \cdot 13.52 \cdot \cos (0.2309)}{29 + 13.52} \cdot 9.8066

Next Step Evaluate

∴

a i = 5.24630963428157m/s²

LAST Step Rounding Answer

∴

a i = 5.2463m/s²

Acceleration of System with Bodies One Hanging Free, Other Lying on Rough Inclined Plane Formula Elements

Variables

Constants

Functions

Acceleration of System in Inclined Plane

Acceleration of System in Inclined Plane is the rate of change of velocity of an object hanging by a string on an inclined plane.

Symbol: a_i

Measurement: AccelerationUnit: m/s²

Note: Value can be positive or negative.

Formulas to find Acceleration of System in Inclined 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

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

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

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)

cos

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

Syntax: cos(Angle)

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 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)

Go Mass of Body B given Frictional Force

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

How to Evaluate Acceleration of System with Bodies One Hanging Free, Other Lying on Rough Inclined Plane?

Acceleration of System with Bodies One Hanging Free, Other Lying on Rough Inclined Plane evaluator uses Acceleration of System in Inclined Plane = (Mass of Left Body-Mass of Right Body*sin(Inclination of Plane)-Coefficient of Friction for Hanging String*Mass of Right Body*cos(Inclination of Plane))/(Mass of Left Body+Mass of Right Body)*[g] to evaluate the Acceleration of System in Inclined Plane, Acceleration of System with Bodies One Hanging Free, Other Lying on Rough 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 rough inclined plane, under the influence of gravity and friction. Acceleration of System in Inclined Plane is denoted by a_i symbol.

How to evaluate Acceleration of System with Bodies One Hanging Free, Other Lying on Rough Inclined Plane using this online evaluator? To use this online evaluator for Acceleration of System with Bodies One Hanging Free, Other Lying on Rough Inclined Plane, enter Mass of Left Body (m₁), Mass of Right Body (m₂), Inclination of Plane (θ_p) & Coefficient of Friction for Hanging String (μ_hs) and hit the calculate button.

FAQs on Acceleration of System with Bodies One Hanging Free, Other Lying on Rough Inclined Plane

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

The formula of Acceleration of System with Bodies One Hanging Free, Other Lying on Rough Inclined Plane is expressed as Acceleration of System in Inclined Plane = (Mass of Left Body-Mass of Right Body*sin(Inclination of Plane)-Coefficient of Friction for Hanging String*Mass of Right Body*cos(Inclination of Plane))/(Mass of Left Body+Mass of Right Body)*[g]. Here is an example- 5.24631 = (29-13.52*sin(0.230907060038806)-0.24*13.52*cos(0.230907060038806))/(29+13.52)*[g].

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

With Mass of Left Body (m₁), Mass of Right Body (m₂), Inclination of Plane (θ_p) & Coefficient of Friction for Hanging String (μ_hs) we can find Acceleration of System with Bodies One Hanging Free, Other Lying on Rough Inclined Plane using the formula - Acceleration of System in Inclined Plane = (Mass of Left Body-Mass of Right Body*sin(Inclination of Plane)-Coefficient of Friction for Hanging String*Mass of Right Body*cos(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), Cosine (cos) function(s).

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

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

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

Acceleration of System with Bodies One Hanging Free, Other Lying on Rough 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, Other Lying on Rough Inclined Plane can be measured.

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