Momentum – The Basics Momentum is mass in motion (or inertia in motion) Momentum is abbreviated as the letter p! Momentum is mass x velocity (p = mv) Both mass and velocity are needed to have momentum The units of Momentum are kg•m/s or N•s

Historical Connections Newton’s 2nd Law (F = ma) was originally written in terms of momentum where: The familiar form is derived by writing the Law as: ΣF = Δp Δt Δv Δt ΣF = mvF-mvI = m ΣF = Δp Δt = ma Δv Δt = a since We can conclude:

Impulse momentum changes due to a force force x time = impulse impulse is the change in momentum F Δt = Δ (m v) = m Δv (most of the time) Δv Δt F = m Force (N) time (s)

Impulse at work Increase momentum of ball Decrease momentum in a crash high force (swing hard) long time (follow through on swing) Decrease momentum in a crash long time during crash reduces force for same momentum F Δt = Δ(m v)

Bouncing Bouncing causes greater change in momentum Greater impulse to reverse direction than just to stop it

Linear Momentum Velocity in a straight line One dimensional along x or y axis Two dimensional some components of velocity in both x and y axis

The System A system is a collection of objects. A system is closed when objects do not enter or leave it. (Similar to a class where students cannot add or drop.) Isolated systems cannot have any external forces acting upon them. A system that is both closed and isolated is needed to study momentum changes in collisions

Conservation of Momentum The Law: In the absence of an external force, the momentum of a system remains unchanged. Internal forces do not change total momentum. Momentum is a vector (has direction).

Collisions net momentum before collision equals net momentum after collision. Elastic collision no permanent deformation no heat objects separate after collision Inelastic collision objects become distorted heat objects stick together

Equations for Collisions Elastic Collision (bouncy, objects separate at beginning and end) m1v1i + m2v2i = m1v1f + m2v2f Inelastic Collision (sticky) m1v1i + m2v2i = (m1 + m2)vf If an object splits into two pieces…the explosion! (m1 + m2)vi = m1v1f + m2v2f

Example Problem 1 A 5.0 kg bowling ball with a velocity of 0.50 m/s rolls into a 6.5 kg bowling ball at rest. After the collision, the second ball travels at 0.43 m/s. What is the velocity of the first ball after the collision?

Example Problem 2 A 2500-kg van traveling at 14 m/s runs into the back of a 910-kg car at rest. The vehicles stick together after the collision. What is the final velocity?

Momentum is a vector momentum vectors of the objects before the collision equal the momentum vectors of the objects after the collision