Question

if the momentum of a body id increased by 50 % calculate % age increase in linear momentum.

Answer 1

$intial \: momentum = mv \\ increased \: momentum = 50 \div 100 \: \: \times mv \\1 \div 2 \: \: mv \\ final \: momentum \: = 1 \div 2 \: mv + mv \: \\ = 3 \div 2 \: \: \: mv \\ \\ mass \: is \: constant \: so \: the \: percentage \: \\ increased \: in \: momentum \: will \: be \: increase \\ in \: velocity \\ so \: if \: \: momentum \: increased \: by \: 3 \div 2 \: \: mv \: so \\ v \: will \: be \: inceased \: by \: 3 \div 2 \: \: \\ if \: ke \: intial \: 1 \div 2 \: \: mv {}^{2} so \: ke - \: kinetic \: energy \\ final \: = \: 1 \div 2 \: m \: (3 \div 4 ) { \\ }^{2} \: v {}^{2} \\ 1 \div 2 \: \: m \: 9v {}^{2} \div 4 \\ percentage \: increased \: in \: ke \: \\ is \: ke \: final \: - ke \: intial \times 100\div ke \: intial \: \\ 1 \div 2 m9 \div 4 \: \: v { \: \\ }^{2} \times 100\: \: m \: - \\ 1 \div 2 \: \: mv {}^{2} \\ 1 \div 2m5 v {}^{2} \times 100 \div 4 \\ so \: increase \: in \: ke \: is \: 125 \: percent \:$