1 - 4 Momentum
● ***Definition: measure of how difficult it is to stop something that is moving
● *** p(momentum [kg m/s ])=m(mass[kg ])∗v(velocity [ m/ s])
● Initial momentum of object = m u
Final momentum of object = m v
∵ Increase/change in momentum = mv −mu
mv −mu
Rate of increase of momentum =
t
mv −mu (change ∈momentum)
∴ *** F (force )=
t (timetaken)
( v−u)
(Since =a, Then F=ma )
t
Δv m(v −u) mv−mu Δ p
● F=ma=m
Δt
=
Δt
=
Δt
=
Δt
○ i.e.: ***Ns = kgm/s
2
p (momentum squared [kg m /s ])
● *** KE (kinetic energy [J ])=
2∗m(mass [kg])
1 2
○ ALSO: *** KE= ∗m(mass [kg])∗v (velocity squared [m/ s])
2
Momentum and collisions
● ***Total momentum of objects which collide remains the same, i.e.: momentum
before collision = momentum after collision
○ ∴ ***Momentum is always conserved, i.e.: m1v1 = m2v2
● ***Impulse (change in momentum): product of (force * time)
● Momentum is a vector, ∴ has direction - i.e.: ∵ going east is momentum 40
kgm/s, ∴ going west is momentum -40 kgm/s
● Elastic collisions {COMPLETE rebound}
○ ***Kinetic energy conserved
○ → Inelastic: objects stick together
○ → Partially elastic: object rebound, but some kinetic energy lost
Factors affecting theoretical momentum***
● Friction (e.g.: between trolleys and track)
● Energy - small amounts of heat lost to surroundings (due to friction ↑)
● Air resistance
● Weight of objects (related to GPE)
○ E.g.: if two trolleys are of different masses, then it would be another story......
1
● ***Definition: measure of how difficult it is to stop something that is moving
● *** p(momentum [kg m/s ])=m(mass[kg ])∗v(velocity [ m/ s])
● Initial momentum of object = m u
Final momentum of object = m v
∵ Increase/change in momentum = mv −mu
mv −mu
Rate of increase of momentum =
t
mv −mu (change ∈momentum)
∴ *** F (force )=
t (timetaken)
( v−u)
(Since =a, Then F=ma )
t
Δv m(v −u) mv−mu Δ p
● F=ma=m
Δt
=
Δt
=
Δt
=
Δt
○ i.e.: ***Ns = kgm/s
2
p (momentum squared [kg m /s ])
● *** KE (kinetic energy [J ])=
2∗m(mass [kg])
1 2
○ ALSO: *** KE= ∗m(mass [kg])∗v (velocity squared [m/ s])
2
Momentum and collisions
● ***Total momentum of objects which collide remains the same, i.e.: momentum
before collision = momentum after collision
○ ∴ ***Momentum is always conserved, i.e.: m1v1 = m2v2
● ***Impulse (change in momentum): product of (force * time)
● Momentum is a vector, ∴ has direction - i.e.: ∵ going east is momentum 40
kgm/s, ∴ going west is momentum -40 kgm/s
● Elastic collisions {COMPLETE rebound}
○ ***Kinetic energy conserved
○ → Inelastic: objects stick together
○ → Partially elastic: object rebound, but some kinetic energy lost
Factors affecting theoretical momentum***
● Friction (e.g.: between trolleys and track)
● Energy - small amounts of heat lost to surroundings (due to friction ↑)
● Air resistance
● Weight of objects (related to GPE)
○ E.g.: if two trolleys are of different masses, then it would be another story......
1
