Angle of Inclination given Acceleration 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%
✖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 Body [a_s]			+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.ⓘ Angle of Inclination given Acceleration [θ_p]

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Angle of Inclination given Acceleration Solution

STEP 0: Pre-Calculation Summary

Formula Used

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]))
θ_p = asin((m₁*[g]-m₁*a_s-m₂*a_s)/(m₂*[g]))
This formula uses 1 Constants, 2 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)
asin - The inverse sine function, is a trigonometric function that takes a ratio of two sides of a right triangle and outputs the angle opposite the side with the given ratio., asin(Number)

Variables Used

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.
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.
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 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.

STEP 1: Convert Input(s) to Base Unit

Mass of Left Body: 29 Kilogram --> 29 Kilogram No Conversion Required
Acceleration of Body: 5.94 Meter per Square Second --> 5.94 Meter per Square Second No Conversion Required
Mass of Right Body: 13.52 Kilogram --> 13.52 Kilogram No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

θ_p = asin((m₁*[g]-m₁*a_s-m₂*a_s)/(m₂*[g])) --> asin((29*[g]-29*5.94-13.52*5.94)/(13.52*[g]))

Evaluating ... ...

θ_p = 0.242392516176502

STEP 3: Convert Result to Output's Unit

0.242392516176502 Radian -->13.8880681624727 Degree (Check conversion here)

FINAL ANSWER

13.8880681624727 ≈ 13.88807 Degree <-- Inclination of Plane

(Calculation completed in 00.035 seconds)

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Home » Physics » Mechanics » Types of Motion » Motion in Bodies Hanging by String » Mechanical » Body Lying on Smooth Inclined Plane » Angle of Inclination given Acceleration

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Created by Vinay Mishra

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

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Verified by Sanjay Krishna

Amrita School of Engineering (ASE), Vallikavu

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< Body Lying on Smooth Inclined Plane Calculators

Angle of Inclination given Acceleration

LaTeX 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

LaTeX 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

LaTeX 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

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

Angle of Inclination given Acceleration Formula

LaTeX Go

Do Inclined Planes reduce Work?

Using an inclined plane makes it easier to move an object. It takes less force to move an object in an upward direction on an inclined plane than it does to lift the object straight up.

How to Calculate Angle of Inclination given Acceleration?

Angle of Inclination given Acceleration calculator uses 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])) to calculate the Inclination of Plane, Angle of Inclination given Acceleration formula is defined as a measure of the angle at which an object is inclined from the horizontal, which affects the acceleration of the object due to gravity and other external forces, and is essential in understanding the motion of objects on inclined planes. Inclination of Plane is denoted by θ_p symbol.

How to calculate Angle of Inclination given Acceleration using this online calculator? To use this online calculator for Angle of Inclination given Acceleration, enter Mass of Left Body (m₁), Acceleration of Body (a_s) & Mass of Right Body (m₂) and hit the calculate button. Here is how the Angle of Inclination given Acceleration calculation can be explained with given input values -> 795.7277 = asin((29*[g]-29*5.94-13.52*5.94)/(13.52*[g])).

FAQ

What is Angle of Inclination given Acceleration?

Angle of Inclination given Acceleration formula is defined as a measure of the angle at which an object is inclined from the horizontal, which affects the acceleration of the object due to gravity and other external forces, and is essential in understanding the motion of objects on inclined planes and is represented as θ_p = asin((m₁*[g]-m₁*a_s-m₂*a_s)/(m₂*[g])) or 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])). Mass of Left Body is the amount of matter in an object hanging from a string, which affects the motion of the system, 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 Right Body is the amount of matter in an object hanging from a string, which affects its motion and oscillations.

How to calculate Angle of Inclination given Acceleration?

Angle of Inclination given Acceleration formula is defined as a measure of the angle at which an object is inclined from the horizontal, which affects the acceleration of the object due to gravity and other external forces, and is essential in understanding the motion of objects on inclined planes is calculated using 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])). To calculate Angle of Inclination given Acceleration, you need Mass of Left Body (m₁), Acceleration of Body (a_s) & Mass of Right Body (m₂). With our tool, you need to enter the respective value for Mass of Left Body, Acceleration of Body & Mass of Right Body and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Inclination of Plane?

In this formula, Inclination of Plane uses Mass of Left Body, Acceleration of Body & Mass of Right Body. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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