Lecture8 (Topic7)
Momentum, Impulse and Collisions
Momentum and Relation to Force
Momentum:
vector quantity
p=mv
Newton's Second Law of Motion
F=ma=m(dv/dt)=dp/dt
Net force applied to an object equals to rate of change of momentum of it
Conservation of Momentum
LAW OF CONSERVATION OF MOMENTUM
The total momentum of an isolated system of objects remains constant.
m₁v₁+m₂v₂=m₁v₁'+m₂v₂'
There are 2 types of force,
internal force and external force.
In Newton's third law of motion,
internal forces cancel each other in pairs.
Impulses
F=dp/dt
dp=Fdt
Impulse, J=△p=Fdt
Impulse=change of momentum
Impulse=area under F/t curve
Collisions
Elastic Collisions:
Conservation of Kinetic Energy
½m₁v₁²+½m₂v₂²=½m₁v₁'²+½m₂v₂'²
v₁-v₂=-(v₁'-v₂')
*valid only for head-on 1D elastic collisions
Inelastic Collisions
Even kinetic energy is not conserved,
total energy is conserved.
K₁+K₂=K₁'+K₂'+thermal and other form of energy
Complete Inelastic Collisions:
-2 objects stick tgt after collision
-MAX KE is transferred to other forms consistent with conservation of momentum
Centre of Mass (CM)
Even object rotates/several parts of system move relative to one another,
there is one point (CM) that moves in the same path that a particle would move if subjected to the same net force.
Xcm=(m₁x₁+m₂x₂)/M
Vcm=(m₁v₁+m₂v₂)/M
2D/3D CENTRE OF MASS
Translational Motion of CM
CM of a system moves like a single particle of mass M acted upon by same net Fext.
System of Variable Mass
NG HUI YUN
A20SC0187