PLEASE SHOW ALL WORK FOR (A) and (B). You may use your class notes, your text bo

Question

PLEASE SHOW ALL WORK FOR (A) and (B).

You may use your class notes, your text book and calculator. No other resources allowed. Mass A ( 0.020 kg), B (0.03 kg) and C (0.05 kg) are moving as in the figure on a frictionless table. All three arrive at the origin. O, at the same time and stick together, What must the x- and y- components of the initial velocity of C be if all three objects end up moving at 0.50 m/s in the +x direction after the collision? what is the change m kinetic energy of the system as a result of the collision?

Explanation / Answer

FOLLOW THIS SOLVED EXAMPLE

the final velocity after collision is
v' = (m1v1 + m2v2)/(m1 + m2)

v' = (mv1 + 4mv2)/(m+4m)
v' = m(v1+ 4v2)/(5m)
v' = (v1 + 4v2)/5 <--- final speed of (mass1 + mass2)
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the initial kinetic energy is
Eki = 1/2 mv1^2 + 1/2 (4m)*v2^2 = 1/2*m(v1^2 + 4v2^2)

the final kinetic energy is
Ekf = 1/2*(5m)*((v1 + 4v2)/5)^2

the change in kinetic energy is
?E = 1/2*m(v1^2 + 4v2^2) - 1/2*(5m)*((v1 + 4v2)/5)^2
simplify to
?E = 2/5*m(v1^2 - 2v1*v2 + v2^2) J = loss in kinetic energy (in kg, m,s system)

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