II. Conservation of Momentum
 Collision/3 Laws
|
In a closed system:
When two objects interact,…….
....the SUM of their momenta BEFORE the interaction ...
...equals the SUM of their momenta AFTER the interaction.
| Total Momentum Before Interaction = Total Momentum After Interaction |
m1v1 + m2v2 = m1v1′ + m2v2′
A) Collision Problems
Ex) A 3.0 kg object traveling 6.0 m/s east has a perfectly elastic collision with a 4.0 kg object traveling 8.0 m/s west. After the collision, the 3.0 kg object will travel 10. m/s west.
a) What was the total momentum before the collision?
Ex 1) A 3.0 kg object traveling 6.0 m/s east has a perfectly elastic collision with a 4.0 kg object traveling 8.0 m/s west. After the collision, the 3.0 kg object will travel 10. m/s west.
a) What was the total momentum before the collision?
| Before | After |
| m1 = 3.0 kg | |
| v1 = 6.0 m/s(East) | |
| m2 = 4.0 kg | |
| v2 = - 8.0 m/s (West) |
Total momentum before:
= m1v1 + m2v2
= 3.0 kg(6.0 m/s)+4 kg(-8 m/s)
= 18. kg(m/s) + -32. kgm/s
= - 14. kg(m/s)
OR 14. kg(m/s) West
Ex 1) A 3.0 kg object traveling 6.0 m/s east has a perfectly elastic collision with a 4.0 kg object traveling 8.0 m/s west. After the collision, the 3.0 kg object will travel 10. m/s west.
b) What is the total momentum of these objects after this collision?
= -14. kg(m/s)
OR 14. kg(m/s) West
Total Momentum Before Interaction = Total Momentum After Interaction
Ex 1) A 3.0 kg object traveling 6.0 m/s east has a perfectly elastic collision with a 4.0 kg object traveling 8. m/s west. After the collision, the 3.0 kg object will travel 10. m/s west.
c) What velocity will the 4.0 kg object have after the collision?
v2′ = ?
Given:
m1 = 3.0 kg
m2 = 4.0 kg
v1′ = -10. m/s
Total Momenta Before Interaction = Total Momenta After Interaction
| Before | After |
-14. kg(m/s) = m1v1′ + m2v2′
-14. kg(m/s) =
3.0 kg(-10.
m/s)+4.0 kg(v2′)
-14. kg(m/s) =
(-30.
kgm/s)+4.0 kg(v2′)
16. kg(m/s) = 4.0 kg(v2′)
v2′ = 4.0 m/s
OR
v2′ = 4.0 m/s East
Ex 2) A 10. kg Block A moves with a velocity of 2.0 m/s to the right and collides with a 10. kg Block B which is at rest. After the collision Block A stops moving and Block B moves to the right.
a) Find the total momentum after the collision
Ex 2) A 10. kg Block A moves with a velocity of 2.0 m/s to the right and collides with a 10. kg Block B which is at rest. After the collision Block A stops moving and Block B moves to the right.
a) Find the total momentum after the collision
| Before | After |
| mA = 10. kg | mA = 10. kg |
| VA = 2.0 m/s (East) | VA′ = 0 m/s |
| mB = 10. kg | mB = 10. kg |
| VB = 0 m/s | VB′ = ? |
Total mom. before = Total mom. after:
= m1v1 + m2v2
= 10. kg(2.0m/s)+10. kg(0 m/s)
= 20 kgm/s
Ex 2) A 10. kg Block A moves with a velocity of 2.0 m/s to the right and collides with a 10. kg Block B which is at rest. After the collision Block A stops moving and Block B moves to the right.
Find the velocity of Block B after the collision.
| Before | After |
| mA = 10. kg | mA = 10. kg |
| vA = 2.0 m/s (East) | vA′ = 0 m/s |
| mB = 10. kg | mB = 10. kg |
| VB = 0 m/s | vB′ = ? |
Total mom. before = Total mom. after:
20. kgm/s = mAVA + mBVB
20. kgm/s =
10. kg(0m/s)+10. kgv2
VB = 2.0 m/s
Ex 3) A 10. kg cart moving with a velocity of 10. m/s East collides and attaches itself to a 10. kg cart moving at a velocity of 50. m/s west.
a) Find the total momentum before the collision
Ex 3) A 10. kg cart moving with a velocity of 10. m/s East collides and attaches itself to a 10. kg cart moving at a velocity of 50. m/s west.
a) Find the total momentum before the collision
| Before | After |
| mA = 10. kg | |
| vA = 10. m/s(East) | |
| m2 = 10. kg | |
| v2 = - 50. m/s |
Total momentum = m1v1 + m2v2
Total momentum =
100. kgm/s + -500. kgm/s
= -4.0 x 102 kgm/s
What is the momentum of the big fish after it swallows the little fish?
-4 kgm/s
Total momentum before = Total momentum after
| p = 15 kgm/s | p = -30 kgm/s |
What is the momentum of the attached carts?
- 15 kgm/s
Ex 3) A 10 kg cart moving with a velocity of 10 m/s East collides and attaches itself to a 10 kg cart moving at a velocity of 50 m/s west.
b) Find the total momentum after the collision
Total mom. before
= Total
mom. after:
= -4.0 x 102 kgm/s
Ex 3) A 10 kg cart moving with a velocity of 10 m/s East collides and attaches itself to a 10 kg cart moving at a velocity of 50 m/s west.
c) What is the velocity of the attached carts after the collision?
| m = 20 kg
(masses combine) |
| v = ? |
Total mom. before =
Total mom. after:
-400. kgm/s = (20. kg)V
V = -20. m/s
V = 20. m/s W
Ex 4) What is the magnitude of the total momentum of these carts?
Total momentum = m1v1 + m2v2
Total mom. =
(4.0 kg)(3 m/s)+6.0kg(-3.0m/s)
= 12. kgm/s + -18. kgm/s
= -6.0 kgm/s
Left train has a momentum of 30 kgm/s, what is the momentum of the right train.
-30 kgm/s