Question Number 29118 by Tinkutara last updated on 04/Feb/18
Commented by Tinkutara last updated on 04/Feb/18
Use the values:
e=3/5
m=7 kg
M=15 kg
u=30 m/s
Theta=30°
Commented by Tinkutara last updated on 04/Feb/18
Thank you very much Sir! I got the answer.
Commented by ajfour last updated on 04/Feb/18
Commented by ajfour last updated on 04/Feb/18
$${v}+{V}\mathrm{sin}\:\theta={eu}\mathrm{sin}\:\theta \\ $$$$\:\:\left({along}\:{normal}\:{to}\:{incline}\:{of}\:{wedge}\right) \\ $$$${MV}+{mu}\mathrm{cos}\:^{\mathrm{2}} \theta−{mv}\mathrm{sin}\:\theta={mu} \\ $$$$\:\:\:\left({momentum}\:{conservation}\right. \\ $$$$\left.\:\:\:\:\:\:\:{along}\:{horizontal}\right) \\ $$$$\Rightarrow\:{MV}−{m}\left({eu}\mathrm{sin}\:\theta−{V}\mathrm{sin}\:\theta\right)\mathrm{sin}\:\theta \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:={mu}\mathrm{sin}\:^{\mathrm{2}} \theta \\ $$$$\:\:\:\boldsymbol{{V}}\:\:=\frac{{mu}\left(\mathrm{1}+{e}\right)\mathrm{sin}\:^{\mathrm{2}} \theta}{{M}+{m}\mathrm{sin}\:^{\mathrm{2}} \theta}\:. \\ $$
Commented by mrW2 last updated on 04/Feb/18
$${e}_{\bot} ={e}=\frac{{V}\:\mathrm{sin}\:\theta+{v}}{{u}\:\mathrm{sin}\:\theta} \\ $$$$\Rightarrow{V}\:\mathrm{sin}\:\theta+{v}={eu}\:\mathrm{sin}\:\theta \\ $$$$ \\ $$$${e}_{//} =\mathrm{1}=\frac{{v}_{//} −{V}\:\mathrm{cos}\:\theta}{{u}\:\mathrm{cos}\:\theta}\:\:\:\left(\ast\right) \\ $$$$\Rightarrow{v}_{//} =\left({u}+{V}\right)\:\mathrm{cos}\:\theta\neq{u}\:\mathrm{cos}\:\theta \\ $$$$ \\ $$$${assume}\:{parallel}\:{restitution}\:{coef}.\:=\mathrm{1} \\ $$
Commented by ajfour last updated on 04/Feb/18
$${ball}\:{did}\:{not}\:{receive}\:{any}\:{impulse} \\ $$$${parallel}\:{to}\:{incline}\:,\:{the}\:{wedge} \\ $$$${did}\:{receieve}\:{an}\:{impulsive}\: \\ $$$${component}\:{from}\:{ground},\: \\ $$$${parallel}\:{to}\:{its}\:{incline},\:{so} \\ $$$${v}_{//} \:\:{of}\:{ball}\:=\:{u}\mathrm{cos}\:\theta \\ $$$${and}\:{not}\:\:{v}_{//} −{V}\mathrm{cos}\:\theta\:=\:{u}\mathrm{cos}\:\theta\:, \\ $$$${Sir}! \\ $$
Answered by ajfour last updated on 04/Feb/18
$${V}_{{M}} =\:\mathrm{5}.\mathrm{04}\:{m}/{s}\:. \\ $$