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현재 위치

Elastic collision of two moving objects, speed after collision

작성자 Uploader : 일상다반사 작성일 Upload Date: 2019-07-17변경일 Update Date: 2019-07-24조회수 View : 334

Type1 Type2

When two objects of mass Ma (kg) and Mb (kg) moving at speeds Vai (m/s) and Vbi collide, the velocity Vaf (m/s) and Vbf (m/s) of two objects after collision can be obtained as follows. Collisions is assumed to be elastic.

Since it is an elastic collision, the momentum and kinetic energy before and after the collision are conserved.

From momentum conservation,

Ma*Vai+Mb*Vbi = Ma*Vaf+Mb*Vbf ………… (1)

Ma*(Vai-Vaf) = Mb*(Vbf-Vbi) ………… (2)

From kinetic energy conservation,

(1/2)*(Ma*Vai^2+Mb*Vbi^2) = (1/2)*(Ma*Vaf^2+Mb*Vbf^2)

Ma*Vai^2+Mb*Vbi^2 = Ma*Vaf^2+Mb*Vbf^2

Ma*(Vai^2-Vaf^2) = Mb*(Vbf^2-Vbi^2)

Ma*(Vai+Vaf)(Vai-Vaf) = Mb*(Vbf+Vbi)(Vbf-Vbi) … (3)

Dividing Equation (3) by Equation (2),

(Vai+Vaf) = (Vbf+Vbi)

Vbf = (Vai+Vaf-Vbi) ………… (4)

Substituting Vbf in Equation (1) with Equation (4),

Ma*Vai+Mb*Vbi = Ma*Vaf+Mb*(Vai+Vaf-Vbi)

(Ma-Mb)*Vai+2*Mb*Vbi = Ma*Vaf+Mb*Vaf

Then,

Vaf = ((Ma-Mb)*Vai+2*Mb*Vbi)/(Ma+Mb)

By a similar manner,

Vaf = (Vbf+Vbi-Vai)

Ma*Vai+Mb*Vbi = Ma*(Vbf+Vbi-Vai)+Mb*Vbf

Then,

Vbf = (2*Ma*Vai+(Mb-Ma)*Vbi)/(Ma+Mb)

■ Input data

▶ Velocity of Object 'a' after collision

▶ Velocity of Object 'b' after collision

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1st Step for All

현재 위치

Elastic collision of two moving objects, speed after collision

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