Tension in String given Mass of Body B Calculator

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Types of Motion

Engineering Mechanics

Friction

General Principal to Dynamics

Properties of Planes and Solids

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Motion in Bodies Connected by Strings

Curvilinear Motion

Linear Motion

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Body Lying on Rough Inclined Plane

Body Lying on Smooth Inclined Plane

Body Passing Over Smooth Pulley

✖Mass of Body B is the measure of the quantity of matter that a body or an object contains.ⓘ Mass of Body B [m_b]			+10% -10%
✖Inclination of Plane 2 is the angle of inclination of a plane measured anticlockwise from the reference horizontal line.ⓘ Inclination of Plane 2 [α₂]			+10% -10%
✖The Coefficient of Friction (μ) is the ratio defining the force that resists the motion of one body in relation to another body in contact with it.ⓘ Coefficient of Friction [μ_cm]			+10% -10%
✖Acceleration of Body in Motion is the rate of change in velocity to the change in time.ⓘ Acceleration of Body in Motion [a_mb]			+10% -10%

✖Tension of String in body B is described as the pulling force transmitted axially by the means of a string.ⓘ Tension in String given Mass of Body B [T_b]

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Formula

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Tension in String given Mass of Body B

Formula

`"T"_{"b"} = "m"_{"b"}*("[g]"*sin("α"_{"2"})+"μ"_{"cm"}*"[g]"*cos("α"_{"2"})+"a"_{"mb"})`

Example

`"13.884N"="1.11kg"*("[g]"*sin("55°")+"0.2"*"[g]"*cos("55°")+"3.35m/s²")`

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Tension in String given Mass of Body B Solution

STEP 0: Pre-Calculation Summary

Formula Used

Tension of String in Body B = Mass of Body B*([g]*sin(Inclination of Plane 2)+Coefficient of Friction*[g]*cos(Inclination of Plane 2)+Acceleration of Body in Motion)
T_b = m_b*([g]*sin(α₂)+μ_cm*[g]*cos(α₂)+a_mb)
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

Tension of String in Body B - (Measured in Newton) - Tension of String in body B is described as the pulling force transmitted axially by the means of a string.
Mass of Body B - (Measured in Kilogram) - Mass of Body B is the measure of the quantity of matter that a body or an object contains.
Inclination of Plane 2 - (Measured in Radian) - Inclination of Plane 2 is the angle of inclination of a plane measured anticlockwise from the reference horizontal line.
Coefficient of Friction - The Coefficient of Friction (μ) is the ratio defining the force that resists the motion of one body in relation to another body in contact with it.
Acceleration of Body in Motion - (Measured in Meter per Square Second) - Acceleration of Body in Motion is the rate of change in velocity to the change in time.

STEP 1: Convert Input(s) to Base Unit

Mass of Body B: 1.11 Kilogram --> 1.11 Kilogram No Conversion Required
Inclination of Plane 2: 55 Degree --> 0.959931088596701 Radian (Check conversion here)
Coefficient of Friction: 0.2 --> No Conversion Required
Acceleration of Body in Motion: 3.35 Meter per Square Second --> 3.35 Meter per Square Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

T_b = m_b*([g]*sin(α₂)+μ_cm*[g]*cos(α₂)+a_mb) --> 1.11*([g]*sin(0.959931088596701)+0.2*[g]*cos(0.959931088596701)+3.35)

Evaluating ... ...

T_b = 13.8840021744081

STEP 3: Convert Result to Output's Unit

13.8840021744081 Newton --> No Conversion Required

FINAL ANSWER

13.8840021744081 ≈ 13.884 Newton <-- Tension of String in Body B

(Calculation completed in 00.004 seconds)

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Home » Physics » Mechanics » Types of Motion » Motion in Bodies Connected by Strings » Body Lying on Rough Inclined Plane » Tension in String given Mass of Body B

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 Maiarutselvan V

PSG College of Technology (PSGCT), Coimbatore

Maiarutselvan V has verified this Calculator and 300+ more calculators!

< 6 Body Lying on Rough Inclined Plane Calculators

Acceleration of System given Mass of Body A

Go Acceleration of Body in Motion = (Mass of Body A*[g]*sin(Inclination of Plane 1)-Coefficient of Friction*Mass of Body A*[g]*cos(Inclination of Plane 1)-Tension of String)/Mass of Body A

Acceleration of System given Mass of Body B

Go Acceleration of Body in Motion = (Tension of String-Mass of Body B*[g]*sin(Inclination of Plane 2)-Coefficient of Friction*Mass of Body B*[g]*cos(Inclination of Plane 2))/Mass of Body B

Tension in String given Mass of Body A

Go 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)

Tension in String given Mass of Body B

Go Tension of String in Body B = Mass of Body B*([g]*sin(Inclination of Plane 2)+Coefficient of Friction*[g]*cos(Inclination of Plane 2)+Acceleration of Body in Motion)

Frictional Force on Body A

Go Frictional Force A = Coefficient of Friction*Mass of Body A*[g]*cos(Inclination of Plane 1)

Frictional Force on Body B

Go Frictional Force B = Coefficient of Friction*Mass of Body B*[g]*cos(Inclination of Plane 2)

Tension in String given Mass of Body B Formula

Is the limiting friction dependent on area of surfaces in contact?

As long as the normal reaction is the same, the magnitude of limiting friction is free of the shape or the area of the surfaces in contact, for any two given surfaces.

How to Calculate Tension in String given Mass of Body B?

Tension in String given Mass of Body B calculator uses Tension of String in Body B = Mass of Body B*([g]*sin(Inclination of Plane 2)+Coefficient of Friction*[g]*cos(Inclination of Plane 2)+Acceleration of Body in Motion) to calculate the Tension of String in Body B, The Tension in string given mass of body B interconnecting two bodies, where both the bodies are lying on rough inclined planes, is the function of the mass of body B, acceleration of the system and the angle of inclination of plane on which body B is lying. Tension of String in Body B is denoted by T_b symbol.

How to calculate Tension in String given Mass of Body B using this online calculator? To use this online calculator for Tension in String given Mass of Body B, enter Mass of Body B (m_b), Inclination of Plane 2 (α₂), Coefficient of Friction (μ_cm) & Acceleration of Body in Motion (a_mb) and hit the calculate button. Here is how the Tension in String given Mass of Body B calculation can be explained with given input values -> 14.75536 = 1.11*([g]*sin(0.959931088596701)+0.2*[g]*cos(0.959931088596701)+3.35).

FAQ

What is Tension in String given Mass of Body B?

The Tension in string given mass of body B interconnecting two bodies, where both the bodies are lying on rough inclined planes, is the function of the mass of body B, acceleration of the system and the angle of inclination of plane on which body B is lying and is represented as T_b = m_b*([g]*sin(α₂)+μ_cm*[g]*cos(α₂)+a_mb) or Tension of String in Body B = Mass of Body B*([g]*sin(Inclination of Plane 2)+Coefficient of Friction*[g]*cos(Inclination of Plane 2)+Acceleration of Body in Motion). Mass of Body B is the measure of the quantity of matter that a body or an object contains, Inclination of Plane 2 is the angle of inclination of a plane measured anticlockwise from the reference horizontal line, The Coefficient of Friction (μ) is the ratio defining the force that resists the motion of one body in relation to another body in contact with it & Acceleration of Body in Motion is the rate of change in velocity to the change in time.

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

The Tension in string given mass of body B interconnecting two bodies, where both the bodies are lying on rough inclined planes, is the function of the mass of body B, acceleration of the system and the angle of inclination of plane on which body B is lying is calculated using Tension of String in Body B = Mass of Body B*([g]*sin(Inclination of Plane 2)+Coefficient of Friction*[g]*cos(Inclination of Plane 2)+Acceleration of Body in Motion). To calculate Tension in String given Mass of Body B, you need Mass of Body B (m_b), Inclination of Plane 2 (α₂), Coefficient of Friction (μ_cm) & Acceleration of Body in Motion (a_mb). With our tool, you need to enter the respective value for Mass of Body B, Inclination of Plane 2, Coefficient of Friction & Acceleration of Body in Motion 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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