Answer to Question #170217 in Mechanics | Relativity for April

Question #170217

A 1-kg ball moving at a velocity of 12 m/s collides head-on with a 2-kg ball moving at 24 m/s

in the opposite direction. Calculate the velocity of each ball after collision if (a) e = 2/3, (b) the

balls stick together, and (c) the collision is perfectly elastic.


1
Expert's answer
2021-03-14T19:18:51-0400

Answer

Given data

u1=24m/su_1=24m/s

u1=12m/su_1=-12m/s

m1=2kgm2=1kgm_1=2kg\\m_2=1kg

Initial momentum

Pi=m1u1+m2u2=4812=36kgm/sec.P_i=m_1u_1+m_2u_2=48-12\\=36kg-m/sec.

Velocitu after collosion

v1=Pi+em2(u2u1)m1+m2v_1=\frac{P_i+em_2(u_2-u_1) }{m_1+m_2}

v2=Pi+em2(u1u2)m2+m1v_2=\frac{P_i+em_2(u_1-u_2) }{m_2+m_1}

a)putting all value

e=2/3

v1=36+2/3×1(1224)2+1=4m/sv_1=\frac{36+2/3\times1(-12-24) }{2+1}=4m/s

v2=36+2/3×1(24+12)2+1=16m/sv_2=\frac{36+2/3\times1(24+12) }{2+1}=16m/s

b) balls stick together

Pi=(m1+m2)vP_i=(m_1+m_2) v

36=(2+1)v36=(2+1) v

v=12m/secv=12m/sec

c) perfectly elastic e=1

v1=36+2/3(1224)2+1=0m/sv_1=\frac{36+2/3(-12-24) }{2+1}=0m/s


v2=36+(24+12)2+1=24m/sv_2=\frac{36+(24+12) }{2+1}=24m/s


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