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Distance traveled until an object stops from falling at height H, using the restitution coefficient

작성자 Uploader : orion 작성일 Upload Date: 2019-11-09변경일 Update Date: 2020-01-07조회수 View : 1017

Find the distance traveled until the object stops from falling at height H.

The coefficient of restitution between the object and the floor is CR.

If the springing height according to the number of springing is called Hn and the distance traveled until it reaches the floor is called Ln, then,

H1 = H * CR ^ 2, L1 = 2 * H * CR ^ 2
H2 = H * CR ^ 4, L2 = 2 * H * CR ^ 4
H3 = H * CR ^ 6, L3 = 2 * H * CR ^ 6

Hn = H * CR ^ (2 * n), Ln = 2 * H * CR ^ (2 * n)

Since Ln is an geometric series with the first term 2 * H * CR ^ 2 and the common ratio CR ^ 2, the sum S is

S = 2 * H * CR ^ 2 * (1-CR ^ (2 * n)) / (1-CR ^ 2)

If n → ∞, then CR ^ (2 * n) → 0,

The distance L traveled to the stop is :

L = H + 2 * H * CR ^ 2 / (1-CR ^ 2)


*** 참고문헌[References] ***
L = H + 2*H*CR^2/(1-CR^2)
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변수명 Variable 변수값 Value 변 수 설 명 Description of the variable


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