Question

A cardinal (Richmondena cardinalis) of mass 4.00×10−2 kg and a baseball of mass 0.146 kg have the same kinetic energy. What is the ratio of the cardinal's magnitude pc of momentum to the magnitude pb of the baseball's momentum? View Available Hint(s)

Answer 1

The ratio of the momentum of the cardinal to baseball is 0.523.

The given parameters;

• mass of the cardinal, m₁ = 4 x 10⁻² kg
• mass of the baseball, m₂ = 0.146 kg

The kinetic energy of the cardinal is calculated as;

$K.E = \frac{1}{2} m_1v_1^2= \frac{1}{2} (4\times 10^{-2})v_1^2$

The kinetic energy of the baseball is calculated as

$K.E = \frac{1}{2} m_2v_2^2= \frac{1}{2} (0.146)v_2^2$

The kinetic energy for both objects are equal;

$\frac{1}{2}(4\times 10^{-2})v_1^2 = \frac{1}{2}(0.146)v_2^2\\\\(4\times 10^{-2})v_1^2 = (0.146)v_2^2\\\\(\frac{v_1}{v_2} )^2 = \frac{0.146}{4\times 10^{-2}} \\\\(\frac{v_1}{v_2} )^2 = 3.65\\\\\frac{v_1}{v_2} = \sqrt{3.65} \\\\\frac{v_1}{v_2} = 1.91$

The momentum of cardinal is calculated as;

$P_1 = m_1 v_1= (4\times 10^{-2})v_1$

The momentum of the baseball is calculated as;

$P_2 = m_2 v_2 = 0.146v_2$

The ratio of the momentum of the cardinal to baseball is calculated as follows;

$\frac{P_1}{P_2} = \frac{(4\times 10^{-2})v_1}{0.146v_2} = \frac{4\times 10^{-2}}{0.146} \times \frac{v_1}{v_2} = \frac{4\times 10^{-2}}{0.146} \times 1.91 = 0.523$

Thus, the ratio of the momentum of the cardinal to baseball is 0.523.

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