The principle of conservation of energy says that the initial energy of the comp

Question

The principle of conservation of energy says that the initial energy of the compressed spring (1/2 kx^2) is transformed into the kinetic energies (1/2 mv^2) of the carts. In the HW you will use conservation of energy and momentum (pimtiai = 0 = p_finai) to derive the following equation for the final velocity of cart 1v_1 _final = squareroot m_2 mx^2 m_1 (m_1 + m_2) Does this equation make sense (mathematically and physically) in the following limits? Show the result mathematically. Do not plug in numbers. m_1 >> m_2 m_1

Explanation / Answer

Given that V1,final = sqrt[(m2*kx^2)/(m1*(m1+m2))]

if m1>>m2

then m1+m2 = m1

and m2/m1 = 0

then V1,final = 0 m/s

if m1<<m2

and m1+m2 = m2

m2/m1 = m2

then v1,final = sqrt[(m2*k*x^2)/m2] = sqrt(k)*x

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