Momentum

Impulse, Linear Momentum, Collisions

Linear Momentum

• Product of mass and linear velocity• Symbol is p; units are kg•m/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

• Fnet= ma = mDv/Dt; so Fnet Dt = mDv

• 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 N•s which equals kg• m/s• When two objects interact, momentum can

be transferred• During interaction, forces on both objects

are the same (3rd 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

• m1v1 + m2v2 = (m1 + m2)vf

• 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

• m1v1i + m2v2i = m1v1f + m2v2f

• ½m1v1i2 +½m2v2i

2 = ½m1v1f2 + ½m2v2f

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