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-4 kgm/s

Total momentum before =
Total momentum after

A) Collision Problems

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 W.

After the collision, the 3.0 kg object will travel 10. m/s west.

a)
Total momentum before the collision?

Ex 1) A 3.0
kg
object traveling 6.0 m/seast 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

m_{1} = 3.0 kg

v_{1} = 6.0 m/s(East)

m_{2} = 4.0 kg

v_{2} = - 8.0 m/s
(West)

Total momentum before:

= m_{1}v_{1}
+ m_{2}v_{2}

= 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

b) What is the
total momentum of these objects
after this collision?

= -14. kg(m/s)

OR14. kg(m/s) West

Total Momentum Before Interaction =
Total Momentum After Interaction

Ex 1) ..... 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?

m_{1}
= 3.0 kg

v_{1}′ = -10. m/s

m_{2}
= 4.0 kg

v_{2}′ = ?

Total Momenta Before
Interaction = Total Momenta After Interaction

Before

After

-14. kg(m/s) = m_{1}v_{1}′
+ m_{2}v_{2}′

-14. kg(m/s) =

3.0 kg(-10. m/s)+4.0
kg(v_{2}′)

-14. kg(m/s) =

(-30. kgm/s)+4.0 kg(v_{2}′)

16. kg(m/s) = 4.0 kg(v_{2}′)

v_{2}′
= 4.0 m/s

OR

v_{2}′
= 4.0 m/s East

What is the
momentum

of the
attached carts?

p = 15 kgm/s

p =
-30 kgm/s

Answer: - 15 kgm/s

Total momentum before = total momentum after

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 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

m_{A}
= 10. kg

m_{A}
= 10. kg

V_{A} = 2.0 m/s (East)

V_{A}′ = 0 m/s

m_{B}
= 10. kg

m_{B}
= 10. kg

V_{B} = 0 m/s

V_{B}′ = ?

Total mom. before = Total
mom. after:

= m_{A}v_{A}
+ m_{B}v_{B}

_{ }

= 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

m_{A} = 10. kg

m_{A} = 10. kg

v_{A} = 2.0 m/s (East)

v_{A}′ = 0 m/s

m_{B} = 10. kg

m_{B} = 10. kg

V_{B} = 0 m/s

v_{B}′ = ?

Total mom. before
= Total mom. after:

20. kgm/s = m_{A}V_{A}
+ m_{B}V_{B}

20. kgm/s =

10. kg(0m/s)+10.
kgV_{2}

V_{B}= 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

m_{A} = 10. kg

v_{A} = 10. m/s(East)

m_{B} = 10. kg

v_{B} = - 50. m/s

Total momentum = m_{1}v_{1}
+ m_{2}v_{2}

Total momentum =

100. kgm/s + -500. kgm/s

= -4.0 x 10^{2} kgm/s

Impulse

Hi-speed video of a
golf ball compressed by driver 00:06 - 3 years ago

Recorded at
10,000 fps with the Photron ultima APX slow motion
video camera, the gold ball can be seen to compress as the golf club
comes into contact with it at high speed. Recorded with the APX as 10K
fps, with a 10 microsecond shutter and 512 (H) x 256 (V) at 10-bit pixel
depth.

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 10^{2} 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?