2-D Momentum, Collisions & Energy
Definition: Momentum -the product of mass and velocity
p  m  v (unit is kg  m / s )
-often called "inertia of motion"
-an object can have inertia, but no momentum
-Newton's Laws of Motion originally defined using the concept of inertia:
Newton’s 1st Law: if a single body has no net force acting on it, momentum is constant or conserved
p  m  v
Newton’s 2nd Law:
(if mass is constant)
Fnet  m  a
 v 
 m

 t 
Fnet  t  mv

p



impuls e- momentum theorem
Fnet  t is called impulse
-often a force is not constant during time its exerted, so use average force
-large impulse ---> large momentum ---> F/t or f/T
Conservation of Momentum
Definition: System -defined collection of objects
Newton's 3rd Law:
total momentum before collision = total momentum after collision
-this applies for closed, isolated systems(objects neither enter or leave it and no external force is exerted)
Law of Conservation of Momentum:
the momentum of any closed, isolated system does not change
total momentum before collision = total momentum after collision
Definition: Work (W) is a measure of energy
W  Fnet  d
{Work = Net Force x distance}
-F is a constant, net force
-d is the magnitude of displacement in direction of F net
-unit of work is Joule (J) or N.m
-work is done only if an object moves in the direction of Fnet
Definition: Energy -non-material property capable of causing changes in matter
2 types of energy:
1. Potential Energy (Ep) -energy of an object due to its position or state or stored energy
 formula: E p  mgh {h is the height of object above 0 m}
2. Kinetic Energy (Ek) -energy of an object due to its motion

formula:
Ek 
1
mv 2
2
- Ep can be converted to Ek
-work is the transfer of energy by mechanical means
-W done on object equals Ek gained by object
-since many objects already have some Ek when W is done on them,
W  E kfinal  E kinitial  E k
{Work - Energy Theorem}
"the net work done on an object is equal to its change in kinetic energy"
if W net is +ve, KE increases
if W net is -ve, KE decreases
Law of Conservation of Energy:
-within a closed, isolated system, energy can change form, but the total amount of energy is constant
E kinitial  E pinitial  E kfinal  E pfinal
Types of Collisions:
1. Elastic Collision…one where the total kinetic energy of the system is conserved.
2. Inelastic Collision…one where the total kinetic energy is not conserved.
-momentum is conserved in both types of collisions
Conditions for elastic collisions:
1. collision must be oblique (initially objects collide at an angle)
2. two objects have identical masses
3. one of the masses is initially stationary
4. the separation angle is a right angle
Solving 2-D Momentum Problems for Oblique Collisions (Tips)
1. Two well-drawn vector diagrams required (one for before and one for after collision)
2. Total (resultant) momentum of an isolated system is conserved regardless of type of collision (elastic or inelastic)
3. Use Pythagorean Theorem/SOHCAHTOA OR Laws of Sines/Cosines
4. Remember, total momentum is conserved, NOT velocity!
Example: A 2.50 x 102 kg stationary bomb explodes into three pieces. One piece with a mass of 1.30 x 10 2 kg moves
north with a velocity of 63.0 m/s. The second piece with mass 65.0 kg moves east with a velocity of 48.0 m/s. What is the
velocity of the third piece?
Example: Two rubber balls with identical masses, one of which is stationary, collide on a frictionless surface. The
moving ball originally has a velocity of 3.0 m/s to the east but after the collision it moves off at an angle of 45o S of E.
Based on this information, determine the velocity of the two balls after the collision, the change in velocity of the ball that
was moving initially AND determine if the collision is elastic.