Answer to Question #284809 in Mechanics | Relativity for Honey ghanghas

Question #284809

A particle of mass π‘šπ‘š collides elastically with a particle of mass 3π‘šπ‘š which is at rest. In the




𝐢𝐢 βˆ’frame, the particle of mass π‘šπ‘š moves with speed 3 π‘šπ‘š/𝑠𝑠 at an angle of 60π‘œπ‘œ after the




collision. Find the final velocity for the mass π‘šπ‘š in the laboratory frame.

1
Expert's answer
2022-01-05T14:30:16-0500

Given quantities:

m1=mm_1=m

m2=3mm_2=3m

v1=v_1= 3ms3 \frac{m}{s}

Ξ±=60o\alpha=60^o

v2=0v_2=0

From conservation of momentum

P1+P2=P1β€²+P2β€²P_1+P_2=P_1^{'}+P_2^{'}

m1v1+m2v2=(m1+m2)Um_1v_1+m_2v_2=(m_1+m_2)U

mv1cos60o+o=4mUmv_1cos60^o+o=4mU

U=3βˆ—0.54=38=0.375msU=\frac{3*0.5}{4}=\frac{3}{8}=0.375\frac{m}{s}


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