Conservation of momentum in two dimensions - Momentum

Conservation of momentum in two dimensions

Lessons

Notes:

In this lesson, we will learn:

  • Review of conservation of momentum
  • Vector nature of momentum and conservation of momentum
  • Problem solving with conservation of momentum in two dimensions

Notes:

  • Momentum is a conserved quantity and a vector.
    • In a collision between a set of objects, total momentum of the objects before collision = total momentum after collision.
    • When using conservation of momentum on objects that move in two dimensions, use vector addition (tip-to-tail method).

Momentum

p=mv:\vec{p} = m \vec{v}: momentum, in kilogram meters per second (kg∙m/s)

m:m: mass, in kilograms (kg)

v:\vec{v}: velocity, in meters per second (m/s)


Impulse

J=FΔt=Δp=mΔv\vec{J} = \vec{F} \Delta t = \Delta \vec{p} = m\Delta \vec{v}

J:\vec{J}: impulse, in newton seconds (N∙s)

F:\vec{F}: force, in newtons (N)

t:\vec{t}: time, in seconds (s)


Conservation of Momentum

pi=pf\sum\vec{p}_i = \sum\vec{p}_f

pi:\vec{p}_i: initial momentum, in kilogram meters per second (kg·m/s)

pf:\vec{p}_f: final momentum, in kilogram meters per second (kg·m/s)


Law of Sines

asinA=bsinB=cSinC\frac{a}{sinA} = \frac{b}{sinB} = \frac{c}{SinC}
a,b,c: length of sides a,b,c
A,B,C: angles opposite sides a, b, c

Law of Cosines

c2=a2+b22abcosCc^2 = a^2 + b^2 - 2ab \,cosC

  • 1.
    pi=pf:\bold{\sum\vec{p}_i = \sum\vec{p}_f}: Objects that bounce apart after collision in two dimensions
  • 2.
    pi=pf:\bold{\sum\vec{p}_i = \sum\vec{p}_f}: Objects that stick together after collision in two dimensions
  • 3.
    pi=pf:\bold{\sum\vec{p}_i = \sum\vec{p}_f}: Objects that explode apart in two dimensions
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Conservation of momentum in two dimensions

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