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

✖Mass of Body A is the amount of matter in an object, a measure of its resistance to changes in its motion.ⓘ Mass of Body A [m_a]			+10% -10%
✖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.ⓘ Angle of Inclination with Body A [α_a]			+10% -10%
✖Mass of Body B is the quantity of matter in an object connected to another body through a string or cord.ⓘ Mass of Body B [m_b]			+10% -10%
✖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.ⓘ Angle of Inclination with Body B [α_b]			+10% -10%

✖Acceleration of Body in Motion is the rate of change of velocity of an object moving in a circular path connected by strings.ⓘ Acceleration of System with Bodies Connected by String and Lying on Smooth Inclined Planes [a_mb]

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Formula

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

Formula

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

Example

3.348792 m/s² = \frac{29.1 kg \cdot \sin (23.11 °) - 1.11 kg \cdot \sin (84.85 °)}{29.1 kg + 1.11 kg} \cdot [g]

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

STEP 0: Pre-Calculation Summary

Formula Used

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]
a_mb = (m_a*sin(α_a)-m_b*sin(α_b))/(m_a+m_b)*[g]
This formula uses 1 Constants, 1 Functions, 5 Variables

Constants Used

[g] - Gravitational acceleration on Earth Value Taken As 9.80665

Functions Used

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., sin(Angle)

Variables Used

Acceleration of Body in Motion - (Measured in Meter per Square Second) - Acceleration of Body in Motion is the rate of change of velocity of an object moving in a circular path connected by strings.
Mass of Body A - (Measured in Kilogram) - Mass of Body A is the amount of matter in an object, a measure of its resistance to changes in its motion.
Angle of Inclination with Body A - (Measured in Radian) - 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.
Mass of Body B - (Measured in Kilogram) - Mass of Body B is the quantity of matter in an object connected to another body through a string or cord.
Angle of Inclination with Body B - (Measured in Radian) - 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.

STEP 1: Convert Input(s) to Base Unit

Mass of Body A: 29.1 Kilogram --> 29.1 Kilogram No Conversion Required
Angle of Inclination with Body A: 23.11 Degree --> 0.403345590135814 Radian (Check conversion here)
Mass of Body B: 1.11 Kilogram --> 1.11 Kilogram No Conversion Required
Angle of Inclination with Body B: 84.85 Degree --> 1.48091187031691 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

a_mb = (m_a*sin(α_a)-m_b*sin(α_b))/(m_a+m_b)*[g] --> (29.1*sin(0.403345590135814)-1.11*sin(1.48091187031691))/(29.1+1.11)*[g]

Evaluating ... ...

a_mb = 3.34879164238414

STEP 3: Convert Result to Output's Unit

3.34879164238414 Meter per Square Second --> No Conversion Required

FINAL ANSWER

3.34879164238414 ≈ 3.348792 Meter per Square Second <-- Acceleration of Body in Motion

(Calculation completed in 00.004 seconds)

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Home » Physics » Mechanics » Types of Motion » Motion in Bodies Connected by Strings » Mechanical » Body Lying on Smooth Inclined Plane » Acceleration of System with Bodies Connected by String and Lying on Smooth Inclined Planes

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Created by Vinay Mishra

Indian Institute for Aeronautical Engineering and Information Technology (IIAEIT), Pune

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Amrita School of Engineering (ASE), Vallikavu

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< Body Lying on Smooth Inclined Plane Calculators

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

Go 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]

Tension in String if Both Bodies are Lying on Smooth Inclined Planes

Go Tension of String = (Mass of Body A*Mass of Body B)/(Mass of Body A+Mass of Body B)*[g]*(sin(Inclination of Plane 1)+sin(Inclination of Plane 2))

Angle of Inclination of Plane with Body A

Go Angle of Inclination with Body A = asin((Mass of Body A*Acceleration of Body in Motion+Tension of String)/(Mass of Body A*[g]))

Angle of Inclination of Plane with Body B

Go Angle of Inclination with Body B = asin((Tension of String-Mass of Body B*Acceleration of Body in Motion)/(Mass of Body B*[g]))

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

What is the direction of Limiting Friction?

The direction of limiting frictional force is always contrary to the direction of motion. Limiting friction acts tangentially to the two surfaces interacting.

How to Calculate 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 calculator 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 calculate 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 calculate Acceleration of System with Bodies Connected by String and Lying on Smooth Inclined Planes using this online calculator? To use this online calculator 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. Here is how the Acceleration of System with Bodies Connected by String and Lying on Smooth Inclined Planes calculation can be explained with given input values -> 3.348792 = (29.1*sin(0.403345590135814)-1.11*sin(1.48091187031691))/(29.1+1.11)*[g].

FAQ

What is 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 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 and is represented as a_mb = (m_a*sin(α_a)-m_b*sin(α_b))/(m_a+m_b)*[g] or 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]. Mass of Body A is the amount of matter in an object, a measure of its resistance to changes in its motion, 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, Mass of Body B is the quantity of matter in an object connected to another body through a string or cord & 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.

How to calculate 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 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 is calculated using 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 calculate Acceleration of System with Bodies Connected by String and Lying on Smooth Inclined Planes, you need 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). With our tool, you need to enter the respective value for Mass of Body A, Angle of Inclination with Body A, Mass of Body B & Angle of Inclination with Body B and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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