Unit 5: Momentum and Collisions
Newton's Third Law of Motion
Learning Targets
- I can identify the action and reaction forces acting in a system.
- I can diagram and calculate the components of force and motion.
- I can calculate and compare the physical property of momentum between two objects.
- I can explain the idea of impulse as it relates to changes in momentum.
- I can apply the law of conservation to momentum of objects involved in ideal collisions.
Questions Based Off of Learning Targets
- If a lady bug flies into a moving car, which would have a greater change in momentum and why?
- Diagram and calculate the components of force and motion.
- If a bowling ball weighing 10 kg and a baseball weighing 5 kg each roll into a set of pins, which would have more momentum when hitting the pins and why?
- If a baseball has momentum and is struck by a bowling ball or a golfball, assuming both the bowling ball and golf ball hit the baseball at the same velocity, which would cause an impulse in momentum of the baseball and why?
- If two cars of equal mass are traveling at different velocities, one at 5 m/s and the other, 15 m/s, what will be their ending velocities after colliding?
Key Concepts
~Forces
- A force is a push or pull that acts upon an object as a result of interaction with other objects
- Contact interactions are normal, frictional, tensional and applied forces
~"For Every Action, There is an Equal but Opposite Reaction"
- In every interaction, there are a pair of forces acting on two interacting objects
- The size of the force on the initial object equals the force on the second object
- The direction of the force of the first and second object are opposite of each other
- Forces always come in equal and opposite action and reaction force pairs
Momentum:
~ Momentum
- Mass in motion
- A quantity describing an objects resistance to stopping
- If an object is in motion, it has momentum
- The amount of momentum an object has depends on how much stuff is moving and how fast it's moving
- Impulse is change in momentum
- Impulse momentum Theorem:
- Large force and small time
- Small force and long time
- Collisions: momentum is conserved, therefore before=after, supporting The Law of Conservation of Momentum
- closed systems: no changes in mass
- Isolated systems: When an external force on a closed system is equal to zero (no applied force from outside)
- No system is truly isolated on earth, so we assume ideal
- Types of Collisions:
- Assume perfect or ideal
- Inelastic- objects collide together and stick, deforming
Ex: Clay being thrown on the ground
- Elastic- objects bounce and spring back into their shape
Ex: Bumper Cars
Vocabulary
~ Elastic- Bounce and spring back into shape
~ Inelastic- Objects that collide and stick together and objects are deformed
~ Impulse- A change in momentum
~ Momentum- Mass in Motion
Formulas
p = m*v
Δp = FΔt = Δp = mΔv
Elastic Collisions:
m1v1 + m2v2 = m1v1+ m2v2
Inelastic Collisions:
m1v1 + m2v2= (m1 + m2)v
- P = Momentum (kg * m/s)
- M =Mass (kilograms)
- V = Velocity (meters/second)
- Δp = impulse (Newtons-seconds)
Practice Problems
Solving:
p=m*v
M=5
V=8
5*8=40
The momentum of the bowling ball is 40 kg * m/s
2. If a car weighing 45 kg going a speed of 50 m/s runs into a car at rest weighing 70 kg and then the first car continues on at 15 m/s, assuming this is an elastic collision, solve for the final velocity of the second car.
m1v1 + m2v2 = m1v1+ m2v2
Initial:
M1=45
V1=50
M2=70
V2=0
Final:
M1=45
V1=15
M2=70
V2=?
45(50) + 70(0) = 45(15) + 70(?)
2250 = 675 + 70(?)
-675 -675
1575 = 70(?)
1575/70 = (70(?))/70
V2 = 22.5 m/s
3. If a toy car weighing 5 kg is hits another toy car at rest weighing 10 kg at the speed of 6 m/s, assuming this is an inelastic collision, find the final velocity of the two cars after colliding.
m1v1 + m2v2= (m1 + m2)v
Initial:
M1=5
V1=6
M2=10
V2=0
Final:
M=15
V= ?
5(6) + 10(0) = (5+10) v
30 = (15) v
30/15 = ((15) v) / 15
V = 2 m/s