8 - Momentum, Impulse, and Collisions Free Online FlashCards

How is a system’s total momentum calculated?

The total momentum of a system is the vector sum of all particle momenta: $\vec p_{\text{system}}=\sum_i m_i\vec v_i$.

What is the impulse-momentum theorem?

Impulse equals the change in momentum: $\vec J=\Delta\vec p=\vec p_f-\vec p_i$. For constant force, $\vec J=\vec F_{\text{net}}\Delta t$.

How is impulse found from a force-time graph?

For a varying force, impulse is the area under the force-versus-time graph: $\vec J=\int \vec F\,dt$.

Why do airbags reduce average collision force?

For a fixed change in momentum, increasing collision time decreases average force because $F_{\text{avg}}=\frac{\Delta p}{\Delta t}$.

When is total momentum conserved?

If the net external impulse is zero, a system’s total momentum remains constant: $\vec p_{\text{initial}}=\vec p_{\text{final}}$.

What effect do internal forces have on total momentum?

Internal forces act between objects inside the chosen system. They can transfer momentum among those objects but cannot change the system’s total momentum by themselves.

What defines an elastic collision?

In an elastic collision, both total momentum and total kinetic energy are conserved. The kinetic energy of an individual object may still change.

What defines an inelastic collision?

An inelastic collision conserves momentum but not total kinetic energy. The lost kinetic energy becomes internal energy, sound, deformation, or other forms.

What happens in a perfectly inelastic collision?

In a perfectly inelastic collision, the objects stick together and share one final velocity: $v_f=\frac{m_1v_{1i}+m_2v_{2i}}{m_1+m_2}$.

Why does a launcher recoil when firing a projectile?

A launcher recoils opposite the projectile so the total momentum remains zero: $0=m_pv_p+m_Lv_L$. Thus, $v_L=-\frac{m_pv_p}{m_L}$.

How is the center of mass found for two particles?

For two particles on one axis, $x_{\text{CM}}=\frac{m_1x_1+m_2x_2}{m_1+m_2}$. The center of mass lies closer to the more massive object.

How are total momentum and center-of-mass velocity related?

Total momentum relates to center-of-mass velocity by $\vec p_{\text{system}}=M\vec v_{\text{CM}}$, where $M$ is the system’s total mass.