Momentum Impulse, Linear Momentum, Collisions

Linear Momentum Product of mass and linear velocity Symbol is p; units are kgm/s p = mv Vector whose direction is same as velocity Related to inertia and kinetic energy Large momentum due to large mass or high speed; no velocity means no momentum

Impulse Net force can change velocity and momentum F net = ma = m  v/  t; so F net  t = m  v Product of force and time interval is impulse Impulse also equals change in momentum due to force

Impulse Must have average or constant force to use this equation Units are Ns which equals kg m/s When two objects interact, momentum can be transferred During interaction, forces on both objects are the same (3 rd law of motion)

Impulse Time interval for interaction is the same for both objects Therefore, impulse must be the same for both objects Short term interactions are called collisions In real collisions forces are usually not constant

Impulse If force is not constant, impulse found by area under force vs. time graph To increase momentum change due to force, increase time force is applied To decrease force in collision, increase time of impact

Conservation of Momentum If no external force acts, and mass doesn’t change, then momentum can’t change Total vector sum of momentum is constant if no external forces act on closed system. Internal forces between objects within system have no effect on total momentum Momentum can be transferred between objects, but sum remains constant.

Collisions Isolated event in which a strong force acts on two or more bodies for a short time. Momentum is transferred, but conserved Two types of collisions, inelastic and elastic Most real collisions are at least partially inelastic

Inelastic Collisions When objects stick together after colliding and/or significant deformation, sound, light are produced In totally inelastic collision, objects stick together, only one final velocity m 1 v 1 + m 2 v 2 = (m 1 + m 2 )v f Energy is not conserved

Elastic Collisions Objects rebound off each other No significant deformation, sound, light, etc. Only true elastic collisions are between gas molecules Kinetic energy and momentum are both conserved Have two initial and two final velocities

Elastic Collision Equations m 1 v 1i + m 2 v 2i = m 1 v 1f + m 2 v 2f ½m 1 v 1i 2 +½m 2 v 2i 2 = ½m 1 v 1f 2 + ½m 2 v 2f 2

Partially Inelastic Collisions Objects bounce off one another but energy is lost to the environment as heat or sound Momentum is conserved

Recoil Events Objects are initially at rest but spring apart due to a release of stored energy Explosion, release of compressed spring, using muscles to push apart, etc. Momentum is conserved Zero momentum initially so total final momentum must also be zero

Two Dimensional Collisions Must use vectors to figure momentum Vector sum of momentum before collision equals vector sum of momentum after collision