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Tension in String given Mass of Body A Formula

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Tension of String in Body A is the force exerted by the string on Body A when it is in motion, affecting its acceleration and movement. Check FAQs

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

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

Tension in String given Mass of Body A Example

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Here is how the Tension in String given Mass of Body A equation looks like with Values.

Here is how the Tension in String given Mass of Body A equation looks like with Units.

Here is how the Tension in String given Mass of Body A equation looks like.

97.7118 = 29.1 \cdot (9.8066 \cdot \sin (34) - 0.2 \cdot 9.8066 \cdot \cos (34) - 0.5)

97.7118N = 29.1kg \cdot (9.8066m/s² \cdot \sin (34°) - 0.2 \cdot 9.8066m/s² \cdot \cos (34°) - 0.5m/s²)

97.7118 = 29.1 \cdot (9.8066 \cdot \sin (34) - 0.2 \cdot 9.8066 \cdot \cos (34) - 0.5)

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Tension in String given Mass of Body A Solution

Follow our step by step solution on how to calculate Tension in String given Mass of Body A?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

T a = 29.1kg \cdot ([g] \cdot \sin (34°) - 0.2 \cdot [g] \cdot \cos (34°) - 0.5m/s²)

Next Step Substitute values of Constants

∴

T a = 29.1kg \cdot (9.8066m/s² \cdot \sin (34°) - 0.2 \cdot 9.8066m/s² \cdot \cos (34°) - 0.5m/s²)

Next Step Convert Units

∴

T a = 29.1kg \cdot (9.8066m/s² \cdot \sin (0.5934rad) - 0.2 \cdot 9.8066m/s² \cdot \cos (0.5934rad) - 0.5m/s²)

Next Step Prepare to Evaluate

∴

T a = 29.1 \cdot (9.8066 \cdot \sin (0.5934) - 0.2 \cdot 9.8066 \cdot \cos (0.5934) - 0.5)

Next Step Evaluate

∴

T a = 97.7117711970527N

LAST Step Rounding Answer

∴

T a = 97.7118N

Tension in String given Mass of Body A Formula Elements

Variables

Constants

Functions

Tension of String in Body A

Tension of String in Body A is the force exerted by the string on Body A when it is in motion, affecting its acceleration and movement.

Symbol: T_a

Measurement: ForceUnit: N

Note: Value can be positive or negative.

Formulas to find Tension of String in Body A

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

Minimum Acceleration of Body in Motion

Minimum Acceleration of Body in Motion is the lowest rate of change of velocity of an object connected to another object by a string.

Symbol: a_min

Measurement: AccelerationUnit: m/s²

Note: Value can be positive or negative.

Formulas to find Minimum Acceleration of Body in Motion

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 in Body Lying on Rough Inclined Plane category

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 Acceleration of System given Mass of Body A

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}

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}

Go Frictional Force on Body A

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

How to Evaluate Tension in String given Mass of Body A?

Tension in String given Mass of Body A evaluator uses Tension of String in Body A = Mass of Body A*([g]*sin(Inclination of Plane 1)-Coefficient of Friction*[g]*cos(Inclination of Plane 1)-Minimum Acceleration of Body in Motion) to evaluate the Tension of String in Body A, Tension in String given Mass of Body A formula is defined as a measure of the force exerted by the string on an object, specifically Body A, which is influenced by the mass of Body A, gravitational acceleration, angle of inclination, and the coefficient of kinetic friction, providing a comprehensive understanding of the string's tension in various physical scenarios. Tension of String in Body A is denoted by T_a symbol.

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

FAQs on Tension in String given Mass of Body A

What is the formula to find Tension in String given Mass of Body A?

The formula of Tension in String given Mass of Body A is expressed as Tension of String in Body A = Mass of Body A*([g]*sin(Inclination of Plane 1)-Coefficient of Friction*[g]*cos(Inclination of Plane 1)-Minimum Acceleration of Body in Motion). Here is an example- 97.71177 = 29.1*([g]*sin(0.59341194567796)-0.2*[g]*cos(0.59341194567796)-0.5).

How to calculate Tension in String given Mass of Body A?

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

Can the Tension in String given Mass of Body A be negative?

Yes, the Tension in String given Mass of Body A, measured in Force can be negative.

Which unit is used to measure Tension in String given Mass of Body A?

Tension in String given Mass of Body A is usually measured using the Newton[N] for Force. Exanewton[N], Meganewton[N], Kilonewton[N] are the few other units in which Tension in String given Mass of Body A can be measured.

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Tension in String given Mass of Body A Formula

Tension in String given Mass of Body A Example

Tension in String given Mass of Body A Solution

Tension in String given Mass of Body A Formula Elements

Other formulas in Body Lying on Rough Inclined Plane category

How to Evaluate Tension in String given Mass of Body A?

FAQs on Tension in String given Mass of Body A

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