Speed deamplifier . In the figure block 1 of mass m 1 slides along an x axis on

Question

Speed deamplifier. In the figure block 1 of mass m1 slides along an x axis on a frictionless floor at speed 7.73 m/s. Then it undergoes a one-dimensional elastic collision with stationary block 2 of mass m2 = 2.16 m1. Next, block 2 undergoes a one-dimensional elastic collision with stationary block 3 of mass m3 = 2.55 m2. (a) What then is the speed of block 3? Are (b) the speed, (c) the kinetic energies, and (d) the momentum of block 3 greater than, less than, or the same as the initial values for block 1?

Explanation / Answer

let m1 = m
u1 = 7.73 m/s
m2 = 2.15*m
u2 = 0
m3 = 2.55*m2

= 2.55*2.15*m

= 5.48*m

a) speed of block2 after the collsion,

v2 = 2*m1*u1/(m1 + m2)

= 2*m*7.73/(m + 2.15*m)

= 4.91 m/s

speed of block3, v3 = 2*m2*v2/(m1+m2)

= 2*2.15*m*4.91/(2.15*m + 5.48*m)

= 2.77 m/s

b) cleraly 2.77 m/s < 7.73 m/s

so, v3 < u1

c) KE3 < KE1

d) P3 < P1

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