Physics - Chapter 7

7.1 §

• Momentum = mass x velocity
  • $\overrightarrow{p}$ = m$\overrightarrow{v}$
  • SI units: kg x $\frac{m}{s}$
• Object’s momentum changes whenever its mass or velocity changes
• Magnitude of Momentum = mass x speed
  • p = mv
  • SI Units: kg x $\frac{m}{s}$
• p and $\overrightarrow{p}$ is sometimes referred to as linear momentum
• ${\overrightarrow{p}}_{total}$ = ${\overrightarrow{p}}_1$ + ${\overrightarrow{p}}_2$ + ${\overrightarrow{p}}_3$ …

7.2 §

• Product of a force and time over which it acts is defined as impluse
  • impulse = force x time interval
  • $\overrightarrow{I}$ = $\overrightarrow{F}$ $△$ t
  • SI Units: N x s = kg x $\frac{m}{s}$
• In cases where direction isn’t important we can use magnitude of force and magnitude of impulse
  • magnitude of impulse = magnitude of force x time
  • I = F$△$ t
  • SI Units: N x s = kg x $\frac{m}{s}$
• When a force acts on an object it changes the object’s momentum, thus there’s a connection between impulse and momentum change
  • General form of Newton’s second law is expressed in terms of momentum as follows: $\overrightarrow{F}$ = $\frac{△\overrightarrow{p}}{△t}$
  • This is how newton originally said force is equal to the rate of change of momentum
• Momentum-Impulse Theorem
  • impulse = force x time = change in momentum
    • $\overrightarrow{I}$ = $\overrightarrow{F}$ $△$ t = $△$ $\overrightarrow{p}$ = m $△$ v

7.3 §

• Momentum of an object can’t change unless an external force acts on the object
• If total force is zero then the initial and final momentums must be the same, which is known as momentum conservation
• Internal Forces - Forces that act between an object between a system
• External Forces - Exerted on a system by something outside the system
• Only external forces can change a system’s momentum, internal forces have no effect
• ${\overrightarrow{F}}_{total}$ = $\sum$ ${\overrightarrow{F}}_{int}$ + $\sum$ ${\overrightarrow{F}}_{ext}$
  • Total force = sum of internal forces and external forces
• Internal forces ALWAYS sum to zero
• ${\overrightarrow{F}}_{total}$ = $\sum$ ${\overrightarrow{F}}_{ext}$
  • Since internal forces always sum to zero the external forces equal the sum of forces
• Momentum-impulse theorem: $\overrightarrow{F}$ $△$ t = ${\overrightarrow{p}}_f$ - ${\overrightarrow{p}}_i$

7.4 §

• Even though momentum is conserved during a collision doesn’t mean that kinetic energy is conserved as well
• Collisions are categorized according to what happens to the kinetic energy of the system, 2 possibilities whether it’s conserved or not
• Elastic Collisions: Collision in which kinetic energy is conserved (unchanged)
• Inelastic Collisions: Kinetic energy changes as a result of the collision
  • Energy is typically converted to sound, heat, and deformation
• Completely inelastic collisions: objects stick together after colliding
• Momentum conservation applies to all collisions
• Total momentum of 2 objects is the sum of mass times velocity for each object
• Equation: ${\overrightarrow{P}}_{total}$ = m${}_1{\overrightarrow{v}}_1$ + m${}_2{\overrightarrow{v}}_2$