Acceleration of System with Bodies One Hanging Free and Other Lying on Smooth Inclined Plane Calculator

✖Mass of Left Body is the amount of matter in an object hanging from a string, which affects the motion of the system.ⓘ Mass of Left Body [m₁]			+10% -10%
✖Mass of Right Body is the amount of matter in an object hanging from a string, which affects its motion and oscillations.ⓘ Mass of Right Body [m₂]			+10% -10%
✖Inclination of Plane is the angle between the plane of motion and the horizontal when a body is hanging by a string.ⓘ Inclination of Plane [θ_p]			+10% -10%

✖Acceleration of Body is the rate of change of velocity of an object hanging by a string, describing its motion under the influence of gravity.ⓘ Acceleration of System with Bodies One Hanging Free and Other Lying on Smooth Inclined Plane [a_s]

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Acceleration of System with Bodies One Hanging Free and Other Lying on Smooth Inclined Plane Solution

STEP 0: Pre-Calculation Summary

Formula Used

Acceleration of Body = (Mass of Left Body-Mass of Right Body*sin(Inclination of Plane))/(Mass of Left Body+Mass of Right Body)*[g]
a_s = (m₁-m₂*sin(θ_p))/(m₁+m₂)*[g]
This formula uses 1 Constants, 1 Functions, 4 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 - (Measured in Meter per Square Second) - Acceleration of Body is the rate of change of velocity of an object hanging by a string, describing its motion under the influence of gravity.
Mass of Left Body - (Measured in Kilogram) - Mass of Left Body is the amount of matter in an object hanging from a string, which affects the motion of the system.
Mass of Right Body - (Measured in Kilogram) - Mass of Right Body is the amount of matter in an object hanging from a string, which affects its motion and oscillations.
Inclination of Plane - (Measured in Radian) - Inclination of Plane is the angle between the plane of motion and the horizontal when a body is hanging by a string.

STEP 1: Convert Input(s) to Base Unit

Mass of Left Body: 29 Kilogram --> 29 Kilogram No Conversion Required
Mass of Right Body: 13.52 Kilogram --> 13.52 Kilogram No Conversion Required
Inclination of Plane: 13.23 Degree --> 0.230907060038806 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

a_s = (m₁-m₂*sin(θ_p))/(m₁+m₂)*[g] --> (29-13.52*sin(0.230907060038806))/(29+13.52)*[g]

Evaluating ... ...

a_s = 5.97481559451083

STEP 3: Convert Result to Output's Unit

5.97481559451083 Meter per Square Second --> No Conversion Required

FINAL ANSWER

5.97481559451083 ≈ 5.974816 Meter per Square Second <-- Acceleration of Body

(Calculation completed in 00.004 seconds)

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Home » Physics » Mechanics » Types of Motion » Motion in Bodies Hanging by String » Mechanical » Body Lying on Smooth Inclined Plane » Acceleration of System with Bodies One Hanging Free and Other Lying on Smooth Inclined Plane

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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

Angle of Inclination given Acceleration

Go Inclination of Plane = asin((Mass of Left Body*[g]-Mass of Left Body*Acceleration of Body-Mass of Right Body*Acceleration of Body)/(Mass of Right Body*[g]))

Acceleration of System with Bodies One Hanging Free and Other Lying on Smooth Inclined Plane

Go Acceleration of Body = (Mass of Left Body-Mass of Right Body*sin(Inclination of Plane))/(Mass of Left Body+Mass of Right Body)*[g]

Angle of Inclination given Tension

Go Inclination of Plane = asin((Tension*(Mass of Left Body+Mass of Right Body))/(Mass of Left Body*Mass of Right Body*[g])-1)

Tension in String when One Body is Lying on Smooth Inclined Plane

Go Tension = (Mass of Left Body*Mass of Right Body)/(Mass of Left Body+Mass of Right Body)*[g]*(1+sin(Inclination of Plane))

Acceleration of System with Bodies One Hanging Free and Other Lying on Smooth Inclined Plane Formula

Acceleration of Body = (Mass of Left Body-Mass of Right Body*sin(Inclination of Plane))/(Mass of Left Body+Mass of Right Body)*[g]
a_s = (m₁-m₂*sin(θ_p))/(m₁+m₂)*[g]

What is the Principle of Inclined Plane?

An inclined plane is a sloping surface, used for raising heavy bodies. The force required to move an object up the incline is less than the weight being raised, discounting friction.

How to Calculate Acceleration of System with Bodies One Hanging Free and Other Lying on Smooth Inclined Plane?

Acceleration of System with Bodies One Hanging Free and Other Lying on Smooth Inclined Plane calculator uses Acceleration of Body = (Mass of Left Body-Mass of Right Body*sin(Inclination of Plane))/(Mass of Left Body+Mass of Right Body)*[g] to calculate the Acceleration of Body, Acceleration of System with Bodies One Hanging Free and Other Lying on Smooth 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 smooth inclined plane, under the influence of gravity. Acceleration of Body is denoted by a_s symbol.

How to calculate Acceleration of System with Bodies One Hanging Free and Other Lying on Smooth Inclined Plane using this online calculator? To use this online calculator for Acceleration of System with Bodies One Hanging Free and Other Lying on Smooth Inclined Plane, enter Mass of Left Body (m₁), Mass of Right Body (m₂) & Inclination of Plane (θ_p) and hit the calculate button. Here is how the Acceleration of System with Bodies One Hanging Free and Other Lying on Smooth Inclined Plane calculation can be explained with given input values -> 5.974816 = (29-13.52*sin(0.230907060038806))/(29+13.52)*[g].

FAQ

What is Acceleration of System with Bodies One Hanging Free and Other Lying on Smooth Inclined Plane?

Acceleration of System with Bodies One Hanging Free and Other Lying on Smooth 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 smooth inclined plane, under the influence of gravity and is represented as a_s = (m₁-m₂*sin(θ_p))/(m₁+m₂)*[g] or Acceleration of Body = (Mass of Left Body-Mass of Right Body*sin(Inclination of Plane))/(Mass of Left Body+Mass of Right Body)*[g]. Mass of Left Body is the amount of matter in an object hanging from a string, which affects the motion of the system, Mass of Right Body is the amount of matter in an object hanging from a string, which affects its motion and oscillations & Inclination of Plane is the angle between the plane of motion and the horizontal when a body is hanging by a string.

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

Acceleration of System with Bodies One Hanging Free and Other Lying on Smooth 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 smooth inclined plane, under the influence of gravity is calculated using Acceleration of Body = (Mass of Left Body-Mass of Right Body*sin(Inclination of Plane))/(Mass of Left Body+Mass of Right Body)*[g]. To calculate Acceleration of System with Bodies One Hanging Free and Other Lying on Smooth Inclined Plane, you need Mass of Left Body (m₁), Mass of Right Body (m₂) & Inclination of Plane (θ_p). With our tool, you need to enter the respective value for Mass of Left Body, Mass of Right Body & Inclination of Plane 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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