Momentum
Beginner
Theorem of Momentum
Source: High school physics (Chinese)
Problem Sets:
momentum - 1111
Problem
Two objects, A and B, have equal kinetic energy. The mass of object A is 4 times the mass of object B.
What is the ratio of the momentum of A to the momentum of B ($p_A : p_B$)?
$p_A : p_B = 2 : 1$
The relationship between kinetic energy $K$ and momentum $p$ is $K = p^2 / (2m)$, which gives $p = \sqrt{2mK}$. The ratio of the momenta is:
$$\frac{p_A}{p_B} = \frac{\sqrt{2m_A K_A}}{\sqrt{2m_B K_B}}$$Given that $K_A = K_B$ and $m_A = 4m_B$, the expression simplifies to:
$$\frac{p_A}{p_B} = \sqrt{\frac{m_A}{m_B}} = \sqrt{\frac{4m_B}{m_B}} = \sqrt{4} = 2$$