Impacts and Linear Momentum ✏ AP Physics 1

Rucete ✏ AP Physics 1 In a Nutshell

6. Impacts and Linear Momentum

This chapter explores linear momentum, impulse, collisions, and center of mass. It covers conservation principles, differences between elastic and inelastic collisions, and how momentum applies in both one and two dimensions.

Momentum and Impulse

• Momentum (p) = m·v; a vector with units kg·m/s.

• Impulse (J) = F·Δt = Δp; also a vector, same units as momentum (N·s).

• Impulse is the change in momentum caused by a force acting over time.

• On a force–time graph, impulse is the area under the curve.

• A large force over short time = same impulse as small force over long time.

• Airbags reduce injury by increasing time, lowering force for the same impulse.

Conservation of Momentum

• In isolated systems (no external force), total momentum is conserved:  p_initial = p_final

• Applies in one or more dimensions (momentum is conserved in each component direction).

• Based on Newton’s third law: action–reaction forces cancel internally.

Elastic vs. Inelastic Collisions

Elastic Collisions

• Momentum and kinetic energy are both conserved.

• Characterized by “rebound” – objects bounce off each other.

• Relative speed before = negative of relative speed after:  v_1i – v_2i = –(v_1f – v_2f)

Inelastic Collisions

• Momentum is conserved, but kinetic energy is not.

• Some KE is transformed into thermal energy, sound, or deformation.

• Completely inelastic: objects stick together and move as one mass.

Sample Problems

1D Momentum Conservation

• Use m₁v₁ + m₂v₂ = m₁v₁′ + m₂v₂′ (for before and after collision).

• If objects stick together:  v_final = (m₁v₁ + m₂v₂)/(m₁ + m₂)

2D Collisions

• Conserve momentum separately in x and y directions.

• Use vector components:  p_xi = p_xf, p_yi = p_yf

• Diagrams and trigonometry help track angles and magnitudes.

Center of Mass (CM)

• The point where an object’s mass is concentrated for analysis of motion.

• For multiple particles:  x_cm = (Σmₙxₙ)/(Σmₙ)

• In projectile motion, the center of mass follows a parabolic path even if the object breaks apart.

• Internal forces (explosions, breaks) do not affect CM motion — it depends only on external forces.

In a Nutshell

Linear momentum is conserved in the absence of external forces, making it a powerful tool for analyzing collisions and interactions. Impulse connects force and momentum change, while elastic and inelastic collisions show how energy is transferred or transformed. Understanding center of mass helps analyze motion of extended objects and systems.