Coefficient of Restitution Calculator

✖Final Velocity of body A after elastic collision, is the last velocity of a given object after a period of time.ⓘ Final Velocity of Body A After Elastic Collision [v₁]			+10% -10%
✖Final Velocity of body B after elastic collision, is the last velocity of a given object after a period of time.ⓘ Final Velocity of Body B After Elastic Collision [v₂]			+10% -10%
✖The initial velocity of body B before the collision is the rate of change of its position with respect to a frame of reference and is a function of time.ⓘ Initial Velocity of Body B Before the Collision [u₂]			+10% -10%
✖The initial velocity of body A before the collision is the rate of change of its position with respect to a frame of reference and is a function of time.ⓘ Initial Velocity of Body A Before the Collision [u₁]			+10% -10%

✖The coefficient of restitution, also denoted by (e), is the ratio of the final to initial relative velocity between two objects after they collide.ⓘ Coefficient of Restitution [e]

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Formula

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Coefficient of Restitution

Formula

`"e" = ("v"_{"1"}-"v"_{"2"})/("u"_{"2"}-"u"_{"1"})`

Example

`"0.833333"=("12m/s"-"8m/s")/("10m/s"-"5.2m/s")`

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Coefficient of Restitution Solution

STEP 0: Pre-Calculation Summary

Formula Used

Coefficient of Restitution = (Final Velocity of Body A After Elastic Collision-Final Velocity of Body B After Elastic Collision)/(Initial Velocity of Body B Before the Collision-Initial Velocity of Body A Before the Collision)
e = (v₁-v₂)/(u₂-u₁)
This formula uses 5 Variables

Variables Used

Coefficient of Restitution - The coefficient of restitution, also denoted by (e), is the ratio of the final to initial relative velocity between two objects after they collide.
Final Velocity of Body A After Elastic Collision - (Measured in Meter per Second) - Final Velocity of body A after elastic collision, is the last velocity of a given object after a period of time.
Final Velocity of Body B After Elastic Collision - (Measured in Meter per Second) - Final Velocity of body B after elastic collision, is the last velocity of a given object after a period of time.
Initial Velocity of Body B Before the Collision - (Measured in Meter per Second) - The initial velocity of body B before the collision is the rate of change of its position with respect to a frame of reference and is a function of time.
Initial Velocity of Body A Before the Collision - (Measured in Meter per Second) - The initial velocity of body A before the collision is the rate of change of its position with respect to a frame of reference and is a function of time.

STEP 1: Convert Input(s) to Base Unit

Final Velocity of Body A After Elastic Collision: 12 Meter per Second --> 12 Meter per Second No Conversion Required
Final Velocity of Body B After Elastic Collision: 8 Meter per Second --> 8 Meter per Second No Conversion Required
Initial Velocity of Body B Before the Collision: 10 Meter per Second --> 10 Meter per Second No Conversion Required
Initial Velocity of Body A Before the Collision: 5.2 Meter per Second --> 5.2 Meter per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

e = (v₁-v₂)/(u₂-u₁) --> (12-8)/(10-5.2)

Evaluating ... ...

e = 0.833333333333333

STEP 3: Convert Result to Output's Unit

0.833333333333333 --> No Conversion Required

FINAL ANSWER

0.833333333333333 ≈ 0.833333 <-- Coefficient of Restitution

(Calculation completed in 00.004 seconds)

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< 17 Kinetics Calculators

Loss of Kinetic Energy during Perfectly Inelastic Collision

Go Loss of K.E During Perfectly Inelastic Collision = (Mass of Body A*Mass of Body B*(Initial Velocity of Body A Before the Collision-Initial Velocity of Body B Before the Collision)^2)/(2*(Mass of Body A+Mass of Body B))

Final Velocity of Bodies A and B after Inelastic Collision

Go Final Speed of A and B After Inelastic Collision = (Mass of Body A*Initial Velocity of Body A Before the Collision+Mass of Body B*Initial Velocity of Body B Before the Collision)/(Mass of Body A+Mass of Body B)

Coefficient of Restitution

Go Coefficient of Restitution = (Final Velocity of Body A After Elastic Collision-Final Velocity of Body B After Elastic Collision)/(Initial Velocity of Body B Before the Collision-Initial Velocity of Body A Before the Collision)

Equivalent Mass Moment of Inertia of Geared System with Shaft A and Shaft B

Go Equivalent Mass MOI of Geared System = Mass Moment of Inertia of Mass Attached to Shaft A+(Gear Ratio^2*Mass Moment of Inertia of Mass Attached to Shaft B)/Gear Efficiency

Kinetic Energy of System after Inelastic Collision

Go Kinetic Energy of System After Inelastic Collision = ((Mass of Body A+Mass of Body B)*Final Speed of A and B After Inelastic Collision^2)/2

Impulsive Force

Go Impulsive Force = (Mass*(Final Velocity-Initial Velocity))/Time Taken to Travel

Loss of Kinetic Energy during Imperfect Elastic Impact

Go Loss of Kinetic Energy During an Elastic Collision = Loss of K.E During Perfectly Inelastic Collision*(1-Coefficient of Restitution^2)

Speed of Guide Pulley

Go Speed of Guide Pulley = Speed of Drum Pulley*Diameter of Drum Pulley/Diameter of Guide Pulley

Centripetal Force or Centrifugal Force for given Angular Velocity and Radius of Curvature

Go Centripetal Force = Mass*Angular Velocity^2*Radius of Curvature

Total Kinetic Energy of Geared System

Go Kinetic Energy = (Equivalent Mass MOI of Geared System*Angular Acceleration of Shaft A^2)/2

Overall Efficiency from Shaft A to X

Go Overall Efficiency from Shaft A to X = Gear Efficiency^Total no. of Gear Pairs

Angular Acceleration of Shaft B given Gear Ratio and Angular Acceleration of Shaft A

Go Angular Acceleration of Shaft B = Gear Ratio*Angular Acceleration of Shaft A

Gear Ratio when Two Shafts A and B are Geared Together

Go Gear Ratio = Speed of Shaft B in RPM/Speed of Shaft A in RPM

Angular Velocity given Speed in RPM

Go Angular Velocity = (2*pi*Speed of Shaft A in RPM)/60

Efficiency of Machine

Go Gear Efficiency = Output Power/Input Power

Power Loss

Go Power Loss = Input Power-Output Power

Impulse

Go Impulse = Force*Time Taken to Travel

Coefficient of Restitution Formula

Why is coefficient of restitution important?

The coefficient of restitution is important because it is what determines whether a collision is elastic or inelastic in nature. During the collision, in a perfect system, the kinetic energy of one object would get transferred to the other object when it collides.

What affects coefficient restitution?

The coefficient of restitution depends to a large extent on the nature of the two materials of which the colliding objects are made. It is also affected by the impact velocity, the shape and size of the colliding objects, the location on the colliding objects at which the collision occurs, and their temperatures.

How to Calculate Coefficient of Restitution?

Coefficient of Restitution calculator uses Coefficient of Restitution = (Final Velocity of Body A After Elastic Collision-Final Velocity of Body B After Elastic Collision)/(Initial Velocity of Body B Before the Collision-Initial Velocity of Body A Before the Collision) to calculate the Coefficient of Restitution, The coefficient of Restitution, also denoted by (e), is the ratio of the final to initial relative velocity between two objects after they collide. A perfectly inelastic collision has a coefficient of 0, but a 0 value does not have to be perfectly inelastic. Coefficient of Restitution is denoted by e symbol.

How to calculate Coefficient of Restitution using this online calculator? To use this online calculator for Coefficient of Restitution, enter Final Velocity of Body A After Elastic Collision (v₁), Final Velocity of Body B After Elastic Collision (v₂), Initial Velocity of Body B Before the Collision (u₂) & Initial Velocity of Body A Before the Collision (u₁) and hit the calculate button. Here is how the Coefficient of Restitution calculation can be explained with given input values -> 0.833333 = (12-8)/(10-5.2).

FAQ

What is Coefficient of Restitution?

The coefficient of Restitution, also denoted by (e), is the ratio of the final to initial relative velocity between two objects after they collide. A perfectly inelastic collision has a coefficient of 0, but a 0 value does not have to be perfectly inelastic and is represented as e = (v₁-v₂)/(u₂-u₁) or Coefficient of Restitution = (Final Velocity of Body A After Elastic Collision-Final Velocity of Body B After Elastic Collision)/(Initial Velocity of Body B Before the Collision-Initial Velocity of Body A Before the Collision). Final Velocity of body A after elastic collision, is the last velocity of a given object after a period of time, Final Velocity of body B after elastic collision, is the last velocity of a given object after a period of time, The initial velocity of body B before the collision is the rate of change of its position with respect to a frame of reference and is a function of time & The initial velocity of body A before the collision is the rate of change of its position with respect to a frame of reference and is a function of time.

How to calculate Coefficient of Restitution?

The coefficient of Restitution, also denoted by (e), is the ratio of the final to initial relative velocity between two objects after they collide. A perfectly inelastic collision has a coefficient of 0, but a 0 value does not have to be perfectly inelastic is calculated using Coefficient of Restitution = (Final Velocity of Body A After Elastic Collision-Final Velocity of Body B After Elastic Collision)/(Initial Velocity of Body B Before the Collision-Initial Velocity of Body A Before the Collision). To calculate Coefficient of Restitution, you need Final Velocity of Body A After Elastic Collision (v₁), Final Velocity of Body B After Elastic Collision (v₂), Initial Velocity of Body B Before the Collision (u₂) & Initial Velocity of Body A Before the Collision (u₁). With our tool, you need to enter the respective value for Final Velocity of Body A After Elastic Collision, Final Velocity of Body B After Elastic Collision, Initial Velocity of Body B Before the Collision & Initial Velocity of Body A Before the Collision 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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