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Acceleration of System with Bodies Connected by String and Lying on Smooth Inclined Planes Formula

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Acceleration of Body in Motion is the rate of change of velocity of an object moving in a circular path connected by strings. Check FAQs

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

a_mb - Acceleration of Body in Motion?m_a - Mass of Body A?α_a - Angle of Inclination with Body A?m_b - Mass of Body B?α_b - Angle of Inclination with Body B?[g] - Gravitational acceleration on Earth?

Acceleration of System with Bodies Connected by String and Lying on Smooth Inclined Planes Example

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Here is how the Acceleration of System with Bodies Connected by String and Lying on Smooth Inclined Planes equation looks like with Values.

Here is how the Acceleration of System with Bodies Connected by String and Lying on Smooth Inclined Planes equation looks like with Units.

Here is how the Acceleration of System with Bodies Connected by String and Lying on Smooth Inclined Planes equation looks like.

3.3488 = \frac{29.1 \cdot \sin (23.11) - 1.11 \cdot \sin (84.85)}{29.1 + 1.11} \cdot 9.8066

3.3488m/s² = \frac{29.1kg \cdot \sin (23.11°) - 1.11kg \cdot \sin (84.85°)}{29.1kg + 1.11kg} \cdot 9.8066m/s²

3.3488 = \frac{29.1 \cdot \sin (23.11) - 1.11 \cdot \sin (84.85)}{29.1 + 1.11} \cdot 9.8066

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Acceleration of System with Bodies Connected by String and Lying on Smooth Inclined Planes Solution

Follow our step by step solution on how to calculate Acceleration of System with Bodies Connected by String and Lying on Smooth Inclined Planes?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

a mb = \frac{29.1kg \cdot \sin (23.11°) - 1.11kg \cdot \sin (84.85°)}{29.1kg + 1.11kg} \cdot [g]

Next Step Substitute values of Constants

∴

a mb = \frac{29.1kg \cdot \sin (23.11°) - 1.11kg \cdot \sin (84.85°)}{29.1kg + 1.11kg} \cdot 9.8066m/s²

Next Step Convert Units

∴

a mb = \frac{29.1kg \cdot \sin (0.4033rad) - 1.11kg \cdot \sin (1.4809rad)}{29.1kg + 1.11kg} \cdot 9.8066m/s²

Next Step Prepare to Evaluate

∴

a mb = \frac{29.1 \cdot \sin (0.4033) - 1.11 \cdot \sin (1.4809)}{29.1 + 1.11} \cdot 9.8066

Next Step Evaluate

∴

a mb = 3.34879164238414m/s²

LAST Step Rounding Answer

∴

a mb = 3.3488m/s²

Acceleration of System with Bodies Connected by String and Lying on Smooth Inclined Planes Formula Elements

Variables

Constants

Functions

Acceleration of Body in Motion

Acceleration of Body in Motion is the rate of change of velocity of an object moving in a circular path connected by strings.

Symbol: a_mb

Measurement: AccelerationUnit: m/s²

Note: Value can be positive or negative.

Formulas to find Acceleration of Body in Motion

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

Angle of Inclination with Body A

Angle of Inclination with Body A is the angle at which Body A is inclined with respect to the horizontal when connected to other bodies by strings.

Symbol: α_a

Measurement: AngleUnit: °

Note: Value can be positive or negative.

Formulas to find Angle of Inclination with 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

Angle of Inclination with Body B

Angle of Inclination with Body B is the angle at which Body B is inclined with respect to the horizontal when connected to another body by a string.

Symbol: α_b

Measurement: AngleUnit: °

Note: Value can be positive or negative.

Formulas to find Angle of Inclination with Body B

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 if Both Bodies are Lying on Smooth Inclined Planes

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

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 Acceleration of System with Bodies Connected by String and Lying on Smooth Inclined Planes?

Acceleration of System with Bodies Connected by String and Lying on Smooth Inclined Planes evaluator uses Acceleration of Body in Motion = (Mass of Body A*sin(Angle of Inclination with Body A)-Mass of Body B*sin(Angle of Inclination with Body B))/(Mass of Body A+Mass of Body B)*[g] to evaluate the Acceleration of Body in Motion, Acceleration of System with Bodies Connected by String and Lying on Smooth Inclined Planes formula is defined as the measure of the acceleration of a system consisting of two bodies connected by a string and lying on smooth inclined planes, where the acceleration is influenced by the masses of the bodies and the angles of the inclined planes. Acceleration of Body in Motion is denoted by a_mb symbol.

How to evaluate Acceleration of System with Bodies Connected by String and Lying on Smooth Inclined Planes using this online evaluator? To use this online evaluator for Acceleration of System with Bodies Connected by String and Lying on Smooth Inclined Planes, enter Mass of Body A (m_a), Angle of Inclination with Body A (α_a), Mass of Body B (m_b) & Angle of Inclination with Body B (α_b) and hit the calculate button.

FAQs on Acceleration of System with Bodies Connected by String and Lying on Smooth Inclined Planes

What is the formula to find Acceleration of System with Bodies Connected by String and Lying on Smooth Inclined Planes?

The formula of Acceleration of System with Bodies Connected by String and Lying on Smooth Inclined Planes is expressed as Acceleration of Body in Motion = (Mass of Body A*sin(Angle of Inclination with Body A)-Mass of Body B*sin(Angle of Inclination with Body B))/(Mass of Body A+Mass of Body B)*[g]. Here is an example- 3.348792 = (29.1*sin(0.403345590135814)-1.11*sin(1.48091187031691))/(29.1+1.11)*[g].

How to calculate Acceleration of System with Bodies Connected by String and Lying on Smooth Inclined Planes?

With Mass of Body A (m_a), Angle of Inclination with Body A (α_a), Mass of Body B (m_b) & Angle of Inclination with Body B (α_b) we can find Acceleration of System with Bodies Connected by String and Lying on Smooth Inclined Planes using the formula - Acceleration of Body in Motion = (Mass of Body A*sin(Angle of Inclination with Body A)-Mass of Body B*sin(Angle of Inclination with Body B))/(Mass of Body A+Mass of Body B)*[g]. This formula also uses Gravitational acceleration on Earth constant(s) and Sine (sin) function(s).

Can the Acceleration of System with Bodies Connected by String and Lying on Smooth Inclined Planes be negative?

Yes, the Acceleration of System with Bodies Connected by String and Lying on Smooth Inclined Planes, measured in Acceleration can be negative.

Which unit is used to measure Acceleration of System with Bodies Connected by String and Lying on Smooth Inclined Planes?

Acceleration of System with Bodies Connected by String and Lying on Smooth Inclined Planes 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 Connected by String and Lying on Smooth Inclined Planes can be measured.

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Acceleration of System with Bodies Connected by String and Lying on Smooth Inclined Planes Formula

Acceleration of System with Bodies Connected by String and Lying on Smooth Inclined Planes Example

Acceleration of System with Bodies Connected by String and Lying on Smooth Inclined Planes Solution

Acceleration of System with Bodies Connected by String and Lying on Smooth Inclined Planes Formula Elements

Other formulas in Body Lying on Smooth Inclined Plane category

How to Evaluate Acceleration of System with Bodies Connected by String and Lying on Smooth Inclined Planes?

FAQs on Acceleration of System with Bodies Connected by String and Lying on Smooth Inclined Planes

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