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Acceleration of System given Mass of Body A Formula

GoAcceleration of System given Mass of Body B 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 [g] \cdot \sin (α 1) - μ cm \cdot m a \cdot [g] \cdot \cos (α 1) - T}{m a}

a_mb - Acceleration of Body in Motion?m_a - Mass of Body A?α₁ - Inclination of Plane 1?μ_cm - Coefficient of Friction?T - Tension of String?[g] - Gravitational acceleration on Earth?[g] - Gravitational acceleration on Earth?

Acceleration of System given Mass of Body A Example

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Here is how the Acceleration of System given Mass of Body A equation looks like with Values.

Here is how the Acceleration of System given Mass of Body A equation looks like with Units.

Here is how the Acceleration of System given Mass of Body A equation looks like.

3.3574 = \frac{29.1 \cdot 9.8066 \cdot \sin (34) - 0.2 \cdot 29.1 \cdot 9.8066 \cdot \cos (34) - 14.56}{29.1}

3.3574m/s² = \frac{29.1kg \cdot 9.8066m/s² \cdot \sin (34°) - 0.2 \cdot 29.1kg \cdot 9.8066m/s² \cdot \cos (34°) - 14.56N}{29.1kg}

3.3574 = \frac{29.1 \cdot 9.8066 \cdot \sin (34) - 0.2 \cdot 29.1 \cdot 9.8066 \cdot \cos (34) - 14.56}{29.1}

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Acceleration of System given Mass of Body A Solution

Follow our step by step solution on how to calculate Acceleration of System given Mass of Body A?

FIRST Step Consider the formula

a mb = \frac{m a \cdot [g] \cdot \sin (α 1) - μ cm \cdot m a \cdot [g] \cdot \cos (α 1) - T}{m a}

Next Step Substitute values of Variables

∴

a mb = \frac{29.1kg \cdot [g] \cdot \sin (34°) - 0.2 \cdot 29.1kg \cdot [g] \cdot \cos (34°) - 14.56N}{29.1kg}

Next Step Substitute values of Constants

∴

a mb = \frac{29.1kg \cdot 9.8066m/s² \cdot \sin (34°) - 0.2 \cdot 29.1kg \cdot 9.8066m/s² \cdot \cos (34°) - 14.56N}{29.1kg}

Next Step Convert Units

∴

a mb = \frac{29.1kg \cdot 9.8066m/s² \cdot \sin (0.5934rad) - 0.2 \cdot 29.1kg \cdot 9.8066m/s² \cdot \cos (0.5934rad) - 14.56N}{29.1kg}

Next Step Prepare to Evaluate

∴

a mb = \frac{29.1 \cdot 9.8066 \cdot \sin (0.5934) - 0.2 \cdot 29.1 \cdot 9.8066 \cdot \cos (0.5934) - 14.56}{29.1}

Next Step Evaluate

∴

a mb = 3.3574491820293m/s²

LAST Step Rounding Answer

∴

a mb = 3.3574m/s²

Acceleration of System given Mass of Body A 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

Inclination of Plane 1

Inclination of Plane 1 is the angle between the plane and the horizontal surface in a system of bodies connected by strings.

Symbol: α₁

Measurement: AngleUnit: °

Note: Value can be positive or negative.

Formulas to find Inclination of Plane 1

Coefficient of Friction

Coefficient of Friction is the ratio of the frictional force resisting motion between two surfaces to the normal force pressing them together.

Symbol: μ_cm

Measurement: NAUnit: Unitless

Note: Value should be between 0 to 1.

Formulas to find Coefficient of Friction

Tension of String

Tension of String is the force exerted by a string on an object, causing it to accelerate or decelerate in a connected system of bodies.

Symbol: T

Measurement: ForceUnit: N

Note: Value can be positive or negative.

Formulas to find Tension of 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

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 to find Acceleration of Body in Motion

Go Acceleration of System given Mass of Body B

a mb = \frac{T - m b \cdot [g] \cdot \sin (α 2) - μ cm \cdot m b \cdot [g] \cdot \cos (α 2)}{m b}

Other formulas in Body Lying on Rough Inclined Plane category

Go Tension in String given Mass of Body A

T a = m a \cdot ([g] \cdot \sin (α 1) - μ cm \cdot [g] \cdot \cos (α 1) - a min)

Go Tension in String given Mass of Body B

T b = m b \cdot ([g] \cdot \sin (α 2) + μ cm \cdot [g] \cdot \cos (α 2) + a mb)

Go Frictional Force on Body A

F A = μ cm \cdot m a \cdot [g] \cdot \cos (α 1)

Go Frictional Force on Body B

F B = μ cm \cdot m b \cdot [g] \cdot \cos (α 2)

How to Evaluate Acceleration of System given Mass of Body A?

Acceleration of System given Mass of Body A evaluator uses Acceleration of Body in Motion = (Mass of Body A*[g]*sin(Inclination of Plane 1)-Coefficient of Friction*Mass of Body A*[g]*cos(Inclination of Plane 1)-Tension of String)/Mass of Body A to evaluate the Acceleration of Body in Motion, Acceleration of System given Mass of Body A formula is defined as a measure of the rate of change of velocity of an object in a system, considering the mass of body A, gravitational force, and frictional forces, allowing for the calculation of the acceleration of the system. Acceleration of Body in Motion is denoted by a_mb symbol.

How to evaluate Acceleration of System given Mass of Body A using this online evaluator? To use this online evaluator for Acceleration of System given Mass of Body A, enter Mass of Body A (m_a), Inclination of Plane 1 (α₁), Coefficient of Friction (μ_cm) & Tension of String (T) and hit the calculate button.

FAQs on Acceleration of System given Mass of Body A

What is the formula to find Acceleration of System given Mass of Body A?

The formula of Acceleration of System given Mass of Body A is expressed as Acceleration of Body in Motion = (Mass of Body A*[g]*sin(Inclination of Plane 1)-Coefficient of Friction*Mass of Body A*[g]*cos(Inclination of Plane 1)-Tension of String)/Mass of Body A. Here is an example- 3.357449 = (29.1*[g]*sin(0.59341194567796)-0.2*29.1*[g]*cos(0.59341194567796)-14.56)/29.1.

How to calculate Acceleration of System given Mass of Body A?

With Mass of Body A (m_a), Inclination of Plane 1 (α₁), Coefficient of Friction (μ_cm) & Tension of String (T) we can find Acceleration of System given Mass of Body A using the formula - Acceleration of Body in Motion = (Mass of Body A*[g]*sin(Inclination of Plane 1)-Coefficient of Friction*Mass of Body A*[g]*cos(Inclination of Plane 1)-Tension of String)/Mass of Body A. This formula also uses Gravitational acceleration on Earth, Gravitational acceleration on Earth constant(s) and , Sine (sin), Cosine (cos) function(s).

What are the other ways to Calculate Acceleration of Body in Motion?

Here are the different ways to Calculate Acceleration of Body in Motion-

Acceleration of Body in Motion=(Tension of String-Mass of Body B*[g]*sin(Inclination of Plane 2)-Coefficient of Friction*Mass of Body B*[g]*cos(Inclination of Plane 2))/Mass of Body B

Can the Acceleration of System given Mass of Body A be negative?

Yes, the Acceleration of System given Mass of Body A, measured in Acceleration can be negative.

Which unit is used to measure Acceleration of System given Mass of Body A?

Acceleration of System given Mass of Body A 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 given Mass of Body A can be measured.

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Acceleration of System given Mass of Body A Formula

​GoAcceleration of System given Mass of Body B Formula

Acceleration of System given Mass of Body A Example

Acceleration of System given Mass of Body A Solution

Acceleration of System given Mass of Body A Formula Elements

Other Formulas to find Acceleration of Body in Motion

Other formulas in Body Lying on Rough Inclined Plane category

How to Evaluate Acceleration of System given Mass of Body A?

FAQs on Acceleration of System given Mass of Body A

Variable Name

GoAcceleration of System given Mass of Body B Formula