Answer:
Explanation:
Given
Mass of block is [tex]M[/tex]
spring constant [tex]=k[/tex]
Amplitude is [tex]A_1[/tex]
when putty is placed then amplitude decreases to [tex]\frac{A_1}{2}[/tex]
Initially [tex]\frac{1}{2}kA^2=\frac{1}{2}Mv^2\quad \ldots(i)[/tex]
Conserving momentum
[tex]Mv_o=(m+M)v[/tex]
where [tex]v_o[/tex]=initial velocity
[tex]v=\frac{M}{M+m}v_o[/tex]
Now
[tex]\frac{1}{2}k(\frac{A_1}{2})^2=\frac{1}{2}(M+m)v^2[/tex]
[tex]\frac{1}{2}k(\frac{A_1}{2})^2=\frac{1}{2}(M+m)(\frac{M}{M+m}v_o)^2\quad \ldots(ii)[/tex]
divide (i) and (ii) we get
[tex]\frac{4}{1}=\frac{M}{M+m}\times (\frac{m+M}{m})^2[/tex]
[tex]4=\frac{m+M}{M}[/tex]
[tex]m=3M[/tex]
Fraction of energy converted into heat[tex]=\frac{1}{2}kA_1^2-\frac{1}{2}k(\frac{A_1}{2})^2[/tex]
[tex]=\frac{1}{2}kA_1^2[1-\frac{1}{4}][/tex]
[tex]=\frac{1}{2}kA_1^2[0.75][/tex]
So, [tex]\frac{3}{4}[/tex] fraction is converted into heat energy
