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AP Physics: Conservation of Momentum — Head-on Elastic Collisions

What Is an Elastic Collision?

Elastic Collision?

↓

No energy lost in collision

(1/2)m1v12 + (1/2)m2v22 = (1/2)m1v1f2 + (1/2)m2v2f2

Combining the Equations

Combine the energy equation above with conservation of momentum

m1v1 + m2v2 = m1v1' + m2v2'

...you get .....

For Head-on Collisions:

V1 - V2 = V2' - V1'

Problem 1

Giancoli — page 189, #23

m1 = .450 kg    V1 = 3.00 m/s

m2 = .900 kg    V2 = 0

↓

Step 1

V1 - V2 = V2' - V1'

V2' - V1' = 3 m/s

V2' = 3 m/s + V1'

Step 2 — Total Mom before = Total Mom After

1.35 kgm/s = .45V1' + .90kg(3 + V1')

1.35 = 1.35V1' + 2.7

↓

V1' = -1 m/s (or 1 m/s West)

Step 3 — Since V2' = 3 m/s + V1', then ...

↓

V2' = 2 m/s East

Collisions in 2 Dimensions

Momentum is conserved
in x and y directions

Total Mom in X direction before = Total Mom in X direction after

Total Mom in Y direction before = Total Mom in Y direction after

If angle between = 90 degrees ... Add vectors using ....

a2 + b2 = c2

Problem 2

Textbook — page 190, #41

Total Momentum Before

Eagle 1:   mv = 4.3 kg(7.8 m/s) = 34 kgm/s

Eagle 2:   mv = 5.6 kg(10.2 m/s) = 57 kgm/s

↓

Total Mom before:

a2 + b2 = c2

342 + 572 = c2

↓

Total mom before = 66 kgm/s

66 kgm/s = (5.6kg + 4.3kg)v

↓

V = 6.7 m/s

problem 42)

Related

Enrichment

Rifle Recoil  —  Dr. Dave's Hall of Fame

Georgia Public Broadcasting Momentum Video