Download Linear Momentum and Conservation of Momentum in Physics - Prof. Wolfgang Losert and more Study notes Physics in PDF only on Docsity!
Phys141 – Mon 10/
- Today: Chapter 9 Momentum
- Administrative:
Experiment 4 this week!
Read rest of chapter 9 (skip 9.7)
Newton’s Second Law revisited
- More general form of Newton’s Second Law using momentum:
Per object: The time rate of change of the linear momentum of an object is equal to the net force acting on the object
For system: The time rate of change of the linear momentum of a system is equal to the sum of forces acting on each object in the system.
d d^^ (^ m ) d
m m
dt dt dt
v v p
F a
Momentum
Chapter 9: Linear Momentum
(Linear) momentum of an object of mass m
moving with a velocity v: p = m v
The total momentum of n objects:
New concept: Conservation of momentum
n i i i
P = (^) ∑ m v
Momentum of interacting particles
Newton’s third law:
Use Newton’s second law:
Mass is constant-> rewrite
AB BA AB BA
F F
or F F
A B
Contact forces during collision FBA (^) F AB
;
0
A B A A B B
A A^ B B
F m dv^ F mdv dt dt dv dv m m dt dt
= =
A A A B
A A B B
dv d m m v dt dt d m v m v dt
=
A B
v Ai v Bi
d
dt
p =
A B
v Af v Bf
System of two objects interacting with ANY force:
Total momentum is conserved (for an isolated system, i.e. a system with no outside forces)!
Example, system of two particles: p Ai + pBi= p Af + p Bf
This can be written as three equations in three dimensions, one for each direction (x,y,z)
Note: The momentum of an individual particle DOES change
x ;^ y ; z
d dt const P const P const P const
P
P
A B
A^ v A^ v B B
v A (^) v B
Conservation of Momentum, examples
- Two sleds on air track (frictionless)
- Physical Laws to understand motion:
- Newton’s Second Law – but no information about F or a
- Energy approach – helps us understand total spring energy is converted into kinetic energy of both sleds, but does not tell which car gets how much energy
- Momentum – does not tell us how much total energy system gets, but tells us how velocity is shared!
-> Need both concepts to find velocities of two carts: Energy and momentum conservation
Types of Collisions
- In an elastic collision, momentum and
kinetic energy are conserved
- In an inelastic collision, kinetic energy is
not conserved, but momentum is still conserved
- If the objects stick together after the collision, it is a perfectly inelastic collision
Elastic Collisions
kinetic energy are conserved
1 1 2 2 1 1 2 2 2 2 1 1 2 2
2 2 1 1 2 2
i i f f
i i
f f
m m
m m
m m
m m
v v
v v
v v
v v
Elastic Collisions, examples
- Example of some special cases
- m 1 = m 2 – the particles exchange velocities
- When a very heavy particle collides head-on with a very light one initially at rest, the heavy particle continues in motion unaltered and the light particle rebounds with a speed of about twice the initial speed of the heavy particle
- When a very light particle collides head-on with a very heavy particle initially at rest, the light particle has its velocity reversed and the heavy particle remains approximately at rest
Perfectly Inelastic Collisions
stick together, they share the same velocity after the collision
( m 1 + m 2 ) v f
