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Momentum and Collisionsand Collisions
Banging things around…Banging things around…
MomentumMomentum
Impact or product of mass and velocityImpact or product of mass and velocityRepresented by the variable “Represented by the variable “””Formula Formula = m v = m vUnits are kg m/sUnits are kg m/s
MOMENTUM IS MASS TIMES MOMENTUM IS MASS TIMES VELOCITYVELOCITY
•More mass means more impactMore mass means more impact•What has more impact – rolling a pingpong ball or bowling ball?What has more impact – rolling a pingpong ball or bowling ball?
•More speed means more impactMore speed means more impact• what has more impact -catching a tossed ball or line drive?what has more impact -catching a tossed ball or line drive?
ImpulseImpulse
The change in momentumThe change in momentumDetermined by the amount of force for how Determined by the amount of force for how
longlongFormula is Formula is p= Ftp= FtClassic example is seatbelt vs dashboard.Classic example is seatbelt vs dashboard.
Seatbelt means slower stop or less forceSeatbelt means slower stop or less forceDashboard means faster stop or more forceDashboard means faster stop or more force
Newton’s Laws of MotionNewton’s Laws of Motion
Change in momentum occurs when force Change in momentum occurs when force is applied. 2nd is applied. 2nd
For every force applied to an object, it For every force applied to an object, it applies each force back. 3rdapplies each force back. 3rd
Conservation of MomentumConservation of Momentum
Momentum cannot be created or Momentum cannot be created or destroyeddestroyed
The results of any collision will not change The results of any collision will not change the the systemsystem momentum momentum
Two objects pushing off each other will Two objects pushing off each other will have the same total momentum as before have the same total momentum as before the actionthe action
CollisionsCollisions
Three types of collisionsThree types of collisionsExplosionsExplosionsInelastic collisionsInelastic collisionsElastic collisionsElastic collisions
Momentum is Momentum is alwaysalways conserved conserved
ExplosionsExplosions
Explosions are collisions where the objects begin as Explosions are collisions where the objects begin as one and then separate into many objects traveling in one and then separate into many objects traveling in different directions.different directions.
All collisions begin with determining the masses All collisions begin with determining the masses involved in the collision. We designate these as minvolved in the collision. We designate these as m11 and and
mm22.. In an explosion, these two masses are added together In an explosion, these two masses are added together
before the explosion. And counted separately after the before the explosion. And counted separately after the explosions.explosions.
After the Explosion…After the Explosion…
The sum of the momentums after the The sum of the momentums after the explosion must equal the sum of the explosion must equal the sum of the momentums before the explosion.momentums before the explosion.
(m(m11 + m + m22)v = m)v = m11vv11 + m + m22vv22
Don’t forget positive and Don’t forget positive and negative directions.negative directions.
Example #1Example #1
A 40-kg boy is sitting on a frozen pond A 40-kg boy is sitting on a frozen pond holding a 4-kg book. The ice is very slick holding a 4-kg book. The ice is very slick and he cannot get off the ice. If he throws and he cannot get off the ice. If he throws the book at 6 m/s. How fast will he travel the book at 6 m/s. How fast will he travel in the opposite direction?in the opposite direction?
MM1 1 = 40 kg M= 40 kg M2 = 2 = 4 kg M4 kg MTT = 44 kg = 44 kg
VV22 = 6 m/s v = 6 m/s vTT = 0 m/s = 0 m/s
(m(m11 + m + m22)v)vTT = m = m11vv11 + m + m22vv22
Inelastic collisionsInelastic collisions
Objects collide and continue as one object Objects collide and continue as one object
– joined like two trains hooked together or – joined like two trains hooked together or
a receiver catching a football.a receiver catching a football.
Formula is Formula is
mm11vv11 + m + m22vv22 = (m = (mTT)v)vTT
Example #2Example #2
Sante throws a 20-kg medicine ball at 10 Sante throws a 20-kg medicine ball at 10 m/s to his friend Frankie weighing a hefty m/s to his friend Frankie weighing a hefty 100 kgs who is moving away from Sante 100 kgs who is moving away from Sante at 2 m/s. Somehow, Santee catches the at 2 m/s. Somehow, Santee catches the ball and falls forward. What speed does ball and falls forward. What speed does he fall forward?he fall forward?
MM1 1 = 20 kg M= 20 kg M2 = 2 = 100 kg M100 kg MTT = 120 kg = 120 kg
V1= 10 m/s VV1= 10 m/s V22 = 2 m/s v = 2 m/s vTT = ? m/s = ? m/s
Elastic collisionsElastic collisions
Objects collide and then bounce off each Objects collide and then bounce off each
other.other.
Formula is:Formula is:
mm11vv11 + m + m22vv2 2 == mm11vv11’’ + m+ m22vv22’ ’
Example #3Example #3
Two 200 kg bumper cars race towards each other at 10 m/s and 15 m/s. After the bump, the slower car moves away at a velocity of 12 m/s. What is the velocity of the faster car?
m1 = 200 kg m2 = 200 kg
V1 = 10 m/s v2 = -15 m/s
V1’ =
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