Momentum with vectors

1
Momentum - with vectors
2
The Principle of Conservation of Linear Momentum
When 2 bodies collide
W1 ms-1
V1 ms-1
m kg
n kg
The total momentum before the total momentum
after
mV1 nW1 mV2 nW2
W2 ms-1
V2 ms-1
m kg
n kg
3
Momentum as a vector
When the velocity is given as a vector .
. the momentum will be a vector.
momentum velocity x mass (4i 5j) ms-1 x 2
kg (8i 10j) kg ms-1

4
Example 1 i
(4i - 2j) ms-1
The red ball (2kg) and blue ball (5kg) collide
(3i 3j) ms-1
What is reds new velocity ?
The total momentum before the total momentum
after
total momentum before blue momentum red
momentum (3i 3j) x 5 (4i - 2j) x
2 (15i 15j) (8i - 4j)
(23i 11j) kg ms-1
5
Example 1 ii
Collision point (glancing blow)
(4i - 2j) ms-1
V ms-1
BEFORE
AFTER
(3i 3j) ms-1
(4i - 2j) ms-1
What is reds new velocity ?
total momentum after blue momentum red
momentum (4i - 2j) x 5 V x 2
(20i - 10j) 2V
The total momentum before the total momentum
after
(23i 11j)
(20i - 10j) 2V
(3i 21j) 2V
V (1.5i 10.5j) ms-1
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Example 2 i
(4i - 2j) ms-1
The red ball (2kg) and blue ball (5kg)
collide and coalesce
(3i 3j) ms-1
total momentum before blue momentum red
momentum (3i 3j) x 5 (4i - 2j) x 2
(15i 15j) (8i - 4j)
(23i 11j) kg ms-1
total momentum after (52) x V 7 x V 7V kg
ms-1
The total momentum before the total momentum
after
(23i 11j) 7V
V (3.3i 1.6j) ms-1
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Activity

• Page 79 of your Mechanics 1 book
• lots more examples
• exercise C
• and the mixed questions (page 80)