## Acceleration of System with Bodies One Hanging Free, Other Lying on Rough Inclined Plane Solution

STEP 0: Pre-Calculation Summary
Formula Used
Acceleration of System in Inclined Plane = (Mass of Left Body-Mass of Right Body*sin(Inclination of Plane)-Coefficient of Friction for Hanging String*Mass of Right Body*cos(Inclination of Plane))/(Mass of Left Body+Mass of Right Body)*[g]
ai = (m1-m2*sin(θp)-μhs*m2*cos(θp))/(m1+m2)*[g]
This formula uses 1 Constants, 2 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)
cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)
Variables Used
Acceleration of System in Inclined Plane - (Measured in Meter per Square Second) - Acceleration of System in Inclined Plane is the rate of change of velocity of an object hanging by a string on an inclined plane.
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.
Coefficient of Friction for Hanging String - Coefficient of Friction for Hanging String is the measure of the frictional force that opposes the motion of a body 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)
Coefficient of Friction for Hanging String: 0.24 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
ai = (m1-m2*sin(θp)-μhs*m2*cos(θp))/(m1+m2)*[g] --> (29-13.52*sin(0.230907060038806)-0.24*13.52*cos(0.230907060038806))/(29+13.52)*[g]
Evaluating ... ...
ai = 5.24630963428157
STEP 3: Convert Result to Output's Unit
5.24630963428157 Meter per Square Second --> No Conversion Required
5.24630963428157 5.24631 Meter per Square Second <-- Acceleration of System in Inclined Plane
(Calculation completed in 00.020 seconds)
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## Credits

Created by Vinay Mishra
Indian Institute for Aeronautical Engineering and Information Technology (IIAEIT), Pune
Vinay Mishra has created this Calculator and 300+ more calculators!
Verified by Sanjay Krishna
Amrita School of Engineering (ASE), Vallikavu
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## <Body Lying on Rough Inclined Plane Calculators

Coefficient of Friction given Tension
​ Go Coefficient of Friction for Hanging String = (Mass of Left Body+Mass of Right Body)/(Mass of Left Body*Mass of Left Body*[g])*Tension in String*sec(Inclination of body)-tan(Inclination of body)-sec(Inclination of body)
Acceleration of System with Bodies One Hanging Free, Other Lying on Rough Inclined Plane
​ Go Acceleration of System in Inclined Plane = (Mass of Left Body-Mass of Right Body*sin(Inclination of Plane)-Coefficient of Friction for Hanging String*Mass of Right Body*cos(Inclination of Plane))/(Mass of Left Body+Mass of Right Body)*[g]
Tension in String given Coefficient of Friction of Inclined Plane
​ Go Tension in String = (Mass of Left Body*Mass of Right Body)/(Mass of Left Body+Mass of Right Body)*[g]*(1+sin(Inclination of Plane)+Coefficient of Friction for Hanging String*cos(Inclination of Plane))
Frictional Force
​ Go Force of Friction = Coefficient of Friction for Hanging String*Mass of Right Body*[g]*cos(Inclination of Plane)

## Acceleration of System with Bodies One Hanging Free, Other Lying on Rough Inclined Plane Formula

Acceleration of System in Inclined Plane = (Mass of Left Body-Mass of Right Body*sin(Inclination of Plane)-Coefficient of Friction for Hanging String*Mass of Right Body*cos(Inclination of Plane))/(Mass of Left Body+Mass of Right Body)*[g]
ai = (m1-m2*sin(θp)-μhs*m2*cos(θp))/(m1+m2)*[g]

## What is Friction?

Friction is defined as a force resisting relative motion and it occurs at the interface between the bodies.

## How to Calculate Acceleration of System with Bodies One Hanging Free, Other Lying on Rough Inclined Plane?

Acceleration of System with Bodies One Hanging Free, Other Lying on Rough Inclined Plane calculator uses Acceleration of System in Inclined Plane = (Mass of Left Body-Mass of Right Body*sin(Inclination of Plane)-Coefficient of Friction for Hanging String*Mass of Right Body*cos(Inclination of Plane))/(Mass of Left Body+Mass of Right Body)*[g] to calculate the Acceleration of System in Inclined Plane, Acceleration of System with Bodies One Hanging Free, Other Lying on Rough 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 rough inclined plane, under the influence of gravity and friction. Acceleration of System in Inclined Plane is denoted by ai symbol.

How to calculate Acceleration of System with Bodies One Hanging Free, Other Lying on Rough Inclined Plane using this online calculator? To use this online calculator for Acceleration of System with Bodies One Hanging Free, Other Lying on Rough Inclined Plane, enter Mass of Left Body (m1), Mass of Right Body (m2), Inclination of Plane p) & Coefficient of Friction for Hanging String hs) and hit the calculate button. Here is how the Acceleration of System with Bodies One Hanging Free, Other Lying on Rough Inclined Plane calculation can be explained with given input values -> 5.24631 = (29-13.52*sin(0.230907060038806)-0.24*13.52*cos(0.230907060038806))/(29+13.52)*[g].

### FAQ

What is Acceleration of System with Bodies One Hanging Free, Other Lying on Rough Inclined Plane?
Acceleration of System with Bodies One Hanging Free, Other Lying on Rough 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 rough inclined plane, under the influence of gravity and friction and is represented as ai = (m1-m2*sin(θp)-μhs*m2*cos(θp))/(m1+m2)*[g] or Acceleration of System in Inclined Plane = (Mass of Left Body-Mass of Right Body*sin(Inclination of Plane)-Coefficient of Friction for Hanging String*Mass of Right Body*cos(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 & Coefficient of Friction for Hanging String is the measure of the frictional force that opposes the motion of a body hanging by a string.
How to calculate Acceleration of System with Bodies One Hanging Free, Other Lying on Rough Inclined Plane?
Acceleration of System with Bodies One Hanging Free, Other Lying on Rough 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 rough inclined plane, under the influence of gravity and friction is calculated using Acceleration of System in Inclined Plane = (Mass of Left Body-Mass of Right Body*sin(Inclination of Plane)-Coefficient of Friction for Hanging String*Mass of Right Body*cos(Inclination of Plane))/(Mass of Left Body+Mass of Right Body)*[g]. To calculate Acceleration of System with Bodies One Hanging Free, Other Lying on Rough Inclined Plane, you need Mass of Left Body (m1), Mass of Right Body (m2), Inclination of Plane p) & Coefficient of Friction for Hanging String hs). With our tool, you need to enter the respective value for Mass of Left Body, Mass of Right Body, Inclination of Plane & Coefficient of Friction for Hanging String 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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