Answer to Question #261302 in Classical Mechanics for kinetics

Question

Big Bob and Little Lulu are stationary. Bob has twice the mass of Lulu. If you push both for the same amount of time with the same force, which of these is true of their momenta (P) and kinetic energies (KE)? Ignore friction (and, hint, think impulse).

a.They have the same KE, but Bob has more P.

b.They have the same P, but Lulu has more KE.

c.Lulu has more P and more KE than Bob.

d.They have the same P and the same KE.

e.Bob has more P and more KE than Lulu.

Answer 1

$m_{bob}=m_1$

$m_{lulu}= m_2$

$m_1 = 2m_2$

$F= ma$

$a_1m_1= a_2m_2$

$a_1 = \frac{a_2}{2}$

$v_1= \frac{v_2}{2}$

$P_1 = m_1v_1= 2m_2*\frac{v_2}{2}= m_2v_2$

$P_2 = m_2v_2$

$P_1 =P_2$

$EK_1= \frac{m_1v_1^2}{2}=\frac{2m_2*\frac{v_2^2}{4}}{2}=\frac{m_2v_2^2}{4}$

$EK_2=\frac{m_2v_2^2}{2}$

$EK_2>EK_1$

$\text{Answer: }b.$