Conservation of Momentum

Newton’s Third Law

• For every action, there is an equal and opposite reaction.

https://www.youtube.com/watch?v=1xQozXJKbGI

https://www.youtube.com/watch?v=y97tlkGohoc

Conservation of Momentum

• Closed system– does not gain or lose mass

– no external forces

• Law of Conservation of Momentum- The momentum of any closed system does not change.

• Velocity is a vector, so that makes Momentum a vector!

• http://www.pbs.org/opb/circus/classroom/circus-physics/linear-momentum/

Collisions

• Elastic- KE does not change

• Happens between hard objects (steel)

• They hit and bounce

• Inelastic- KE decreases (converted to heat)

• Happens between soft, sticky objects (clay)

• They stick together after colliding!

Equations

P = mv

Find the momentum of a 15 kg dog running at 5 m/s:

Elastic Collisions:

• M1V1(initial) + M2V2(initial) = M1V1(final) + M2V2 (final)

Inelastic Collisions:

• M1V1(initial) + M2V2(initial) = (M1 + M2) V(final)

Collision Problems

• Figure out what type of collision is taking place.

• Use the correct equation! (elastic or inelastic?)

• Make sure to identify direction!

• Solve for the unknown variable.

• Two billiard balls are traveling in the same direction. Each has a mass of 500 g. Ball #1 is traveling at 4 m/s, while ball #2 is traveling at 6 m/s. They hit and stick together. How fast are they moving together?

• M1V1(initial) + M2V2(initial) = (M1 + M2) V(final)

• (0.5 kg)(4 m/s) + (0.5 kg)(6 m/s) = (0.5 + 0.5) Vf

• Vf = 5 m/s

• Two bumper cars bounce against each other head-on. One car has a mass of 75 kg and is traveling 6 m/s. The other car has a mass of 65 kg and is traveling 4 m/s. They hit and bounce off each other. If the 75 kg car is moving at 3 m/s after the collision, how fast is the other car moving?

• M1V1(initial) + M2V2(initial) = M1V1(final) + M2V2 (final)

• (75)(6) + (65)(-4) = (75)(-3) + (65) V2 (final)

• V2 (final) = 6.4 m/s

Bellwork

• What is the mass of a duck with a momentum of 135 kg m/s flying at a velocity of 24 m/s?

Two ice skaters, with masses of 45 kg and 65 kg, are at rest and facing each other over a surface of ice. They push off from each other and the 45 kg skater moves away with a velocity of 6 m/s. Find the final velocity

of the 65 kg skater.

Impulse• What does it mean to “follow-through?” in sports?

• Increase the amount of time that the force is in contact with the object

• Leads to greater velocity of object

• The product of Force and the Time over which it is applied is called Impulse (J)

J = FΔt

• F Δt = Δp Impulse is change in momentum

• F Δt = m Δv

• F Δt = m (vf-vi)

A soccer player kicks a 0.1 kg ball that is initially at rest so that it moves with a velocity

of 20 m/s. What is the impulse the player imparts to the ball? If the player’s foot was in contact with the ball for 0.01 s, what was the force exerted by the player’s foot on the ball?

•Minimizing the impact force:•What do you do when you land from a jump of any height? •A boxer moves away from a punch to increase impact time

FΔt = Δp

•Maximizing the impact force:•Hulk smash, karate, etc.

http://www.youtube.com/watch?v=JgF-WDkhkOk&NR=1&feature=endscreen

Tiger Woods hits a 0.050 kg golf ball, giving it a speed of 75 m/s. What impulse does he impart to the ball?