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Height of rise when a mass hanging on a pendulum collides another mass

ÀÛ¼ºÀÚ Uploader : airun ÀÛ¼ºÀÏ Upload Date: 2019-07-16º¯°æÀÏ Update Date: 2019-07-19Á¶È¸¼ö View : 2469

As shown in the figure, assume a mass m (kg) is hanging on a line of length L (m) from the horizontal position with respect to the center of rotation O. Falling from this position, this mass hits another mass M (kg) at the vertical position and becomes a single united mass, then  moves up to the height h (m) from the lowest position. Then, the height h can be obtained as follows.

The speed at which an object of mass m collides with an object of mass M,

v1 = (2*g*L)^(1/2)

If the velocity after collision is v2, according to the law of conservation of momentum,

m*v1 = v2(m+M)*v2

v2 = m*v1/(m+M)

Since the kinetic energy of the united mass at the lowest position is the same as the potential energy in the raised position by the height h,

(1/2)(m+M)v2^2 = (m+M)*g*h

Applying v2 and v1,

(1/2)(m+M)(m*(2*g*L)^(1/2)/(m+M))^2 = (m+M)*g*h

(1/2)(m+M)*m^2*2*g*L/(m+M)^2 = (m+M)*g*h

m^2*L/(m+M) = (m+M)*h

h/L = (m/(m+M))^2

h = L*(m/(m+M))^2


*** Âü°í¹®Çå[References] ***

h = L*(m/(m+M))^2
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