0 Three blocks, are placed on a frictionless surface as shown above. Block A has

Question

0 Three blocks, are placed on a frictionless surface as shown above. Block A has a given mass of m, Block B has a given mass of 2m and Block C has a given mass of 5m. Block A has initial velocity given as vo while the other two blocks are initially at rest. Then the following happens: . First Collision: Block A collides with Block B and this collision is totally inelastic Second Collision: Block B collides with Block C and this collision is totally elastic. Part (a): Determine the final velocity of every block immediately after the First Collision Part (b): Determine the final velocity of every block immediately after the Second Collision Part (c): Suppose we define VoM as the velocity of the Center-of-Mass of the entire system of three blocks, A, B, and C. What is VoM just before the First collision. What is VoM just after this First Collision? What is VeM just after this Second Collision?

Explanation / Answer

Given

masses are of m1= mA = m , m2= mB = 2m , m3 = mC = 5m

let initial velocity of A is v0 = u1  

and we confined that the collision is head-on collision only so there is no velocity along y direction

first in inelastic collision only the momentum will conserve.

so when m1 collides with m2 , m1 comes to rest , and when m2 collides with m3 , m2 comes to rest

Part A

First collision

m1 collides with m2 ===> m1*u1+m2*u2 = m1*v1+m2*v2

m1*u1+m2*0 = m1*0 + m2*v2

m2*v2 = m1*u1

v2 = m*u1/2m = u1/2 m/s

and v3=0 ,v1=0 m/s

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Part B

Secomd collision , v1=0 ,

m2 collides with m3 ===> m2*u2+m3*u3 = m2*v2+m3*v3

m2*u2+m2*0 = m2*0 + m3*v3

m3*v3 = m2*u2

v3 = m2*u2/m3 =(2m*u1/2)/ 5m m/s = u1/5 m/s

and v3= u1/5 m/s ,v2 = 0 m/s

Part C

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Before the first collison is

VCm = (m1*u1+m2*u2+m3*u3)/(m1+m2+m3)

= (m*v0+0+0)/(m1+m2+m3)

= m*v0 /(m+2m+5m)

= m*v0 /(8m)

= v0/8 m/s

and after the first collision is  

VCm = (m1*v1+m2*v2+m3*v3)/(m1+m2+m3)

= (m*v0+m2*0.5*u1+0)/(m1+m2+m3)

= 2m*0.5*v0 /(m+2m+5m)

= m*v0 /(8m)

= v0/8 m/s

after the second collision

VCm = (m1*v1+m2*v2+m3*v3)/(m1+m2+m3)

= (m*0+m2*0+m3*v3)/(m1+m2+m3)

= (0+0+5m*v0/5) /(m+2m+5m)

= m*v0 /(8m)

= v0/8 m/s

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