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Name: ................................................. Class: ...............
Momentum and collisions
Vocabulary:
1. Momentum: Is the quantity of motion of a moving object. Symbol is 𝒑
2. A system: Is a collection of two or more objects.
3. An isolated system: is a system that F is free from the influence of a net
external force.
4. Impulse: is the change in momentum
is the product of the force and the time
5. Collision: two objects strike one another
6. Elastic collision: the two objects bounces back after collision
7. Inelastic collision: is the collision when objects are deformed or stick
together
Formula 𝑝 = 𝑚𝑣
𝑝(Momentum)
𝑚(Mass)
𝑣 (Velocity)
Momentum increases when either mass or velocity increases
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Impulse
Impulse is the change in momentum, and it can be calculated in two ways:
1. As the product (multiplication) of the force and the time
2. We calculate 𝑝𝑓 and 𝑝𝑖 and subtract
∆𝒑: 𝒊𝒎𝒑𝒖𝒍𝒔𝒆(𝐍. 𝐬)
𝑷𝒊: 𝒊𝒏𝒊𝒕𝒊𝒂𝒍(Kg.m/s)
𝑷𝒇: 𝒇𝒊𝒏𝒂𝒍(𝐊𝐠. 𝐦/𝐬)
𝑭: 𝑭𝒐𝒓𝒄𝒆(𝐍)
𝒕: 𝒕𝒊𝒎𝒆(𝒔)
∆𝒑 = 𝒑𝒇 − 𝒑𝒊 = (𝒎 × 𝒗𝒇) − (𝒎 × 𝒗𝒊)
∆𝒑 = 𝑭 × 𝒕
Example:
A 1400 kg car moving westward with a velocity of 15 m/s collides with a
utility pole and is brought to rest in 0.3 s.
Find the force exerted on the car during the collision.
Given:
𝑚=1400kg
𝑣𝑖=15 m/s to the west which means that vi us negative 𝒗𝒊=—15 m/s
t=0.3s 𝑣𝑓= 0 m/s
Unknown: 𝐹 =?
Equation:
Substitute:
∆𝒑 = (𝒎 × 𝒗𝒇) − (𝒎 × 𝒗𝒊)
∆𝒑 = (𝟏𝟒𝟎𝟎 × 𝟎) − (𝟏𝟒𝟎𝟎 × −𝟏𝟓)
∆𝒑 = 𝟐𝟏𝟎𝟎𝟎 𝑵. 𝒔
∆𝒑 = (𝑭 × 𝒕)
∆𝒑
𝑭=
𝒕
Solution: 𝑭 = 𝟕 × 𝟏𝟎𝟒 𝑵 𝒕𝒐 𝒕𝒉𝒆 𝒆𝒂𝒔𝒕
Substitute:
𝟐𝟏𝟎𝟎𝟎
𝑭=
𝟎. 𝟑
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THE LAW OF MOMENTUM CONSERVATION.
For a collision occurring between object 1 and object 2 in an isolated system,
the total momentum of the two objects before the collision IS EQUAL to the
total momentum of the two objects after the collision.
Which means:
𝒑𝟏𝒊 + 𝒑𝟐𝒊 = 𝒑𝟏𝒇 + 𝒑𝟐𝒇
𝒑𝒊 = 𝒑𝒇
i: initial(before collision)
1: first object
f: final ( after collision)
2: second object
For example,
𝑝1𝑖 is the initial momentum of object 1
𝑝2𝑓 is the final momentum of object 2
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Inelastic collision
Is the collision when objects are
deformed or stick together.
Before collision
After collision and deformation
When using this equation, it is important to pay attention to the SIGNS that
indicate direction
In the picture above v1i has positive value (m1 is moving to the right)
While v2i has negative value (m2 is moving the left)
To find final velocity (after collision )
𝒎𝟏 𝒗𝟏𝒊 + 𝒎𝟐 𝒗𝟐𝒊
𝒗𝒇 =
𝒎𝟏 + 𝒎𝟐
Note that inelastic collision has only one final velocity
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Example:
A 1850 kg luxury sedan stopped at a traffic light is struck from
the rear by a compact car with a mass of 975 kg.
The two cars become entangled as a result of the collision. If the
compact car was moving at a velocity of 22 m/s to the north before
the collision, what is the velocity of the entangled cars after the
collision?
Given: m1 = 1850 kg, m2 = 975 kg , v1i = 0 m/s, v2i = 22.0 m/s to
the north Unknown: vf = ?
𝒗𝒇 =
𝒎𝟏 𝒗𝟏𝒊 + 𝒎𝟐 𝒗𝟐𝒊
𝒎𝟏 + 𝒎𝟐
(𝟏𝟖𝟓𝟎)(𝟎) + (𝟗𝟕𝟓)(𝟐𝟐)
𝒗𝒇 =
𝟏𝟖𝟓𝟎 + 𝟗𝟕𝟓
𝒗𝒇 = 𝟕. 𝟓𝟗 𝒎/𝒔
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Elastic collision
Elastic collision s the collision in which two objects collide and return to their
original shapes with no loss of total kinetic energy.
After the collision, the two objects move separately.
Both the total momentum and the total kinetic energy are conserved.
𝑣1𝑓 =
𝑣2𝑓
𝑚1 𝑣1𝑖 + 𝑚2 𝑣2𝑖 − 𝑚2 𝑣2𝑓
𝑚1
𝑚1 𝑣1𝑖 + 𝑚2 𝑣2𝑖 − 𝑚1 𝑣1𝑓
=
𝑚2
Example 1
Taiba rolls a 7-kg bowling ball down the alley for the league championship.
One pin is still standing, and Taiba hits it head-on with a velocity of 9 m/s.
The 2 kg pin acquires a forward velocity of 14 m/s. What is the new velocity
of the bowling ball?
Object1 (i)
Object1 (f)
Object2 (i) Object2 (f)
Before
After
Before
After
Bowling Ball
Bowling Ball
pin
pin
𝒗𝟏𝒊= 9 m/s
𝒗𝟏𝒇= ?
𝒗𝟐𝒊=
0 m/s
𝒎𝟏 =7 kg
𝒗𝟐𝒇 =
14 m/s
𝒎𝟐 =2 kg
𝑚1𝑣1𝑖 + 𝑚2𝑣2𝑖 − 𝑚2𝑣2𝑓
𝑚1
(7)(9) + (2)(0) − (2)(14)
𝑣1𝑓 =
= 5 m/s
7
𝑣1𝑓 =
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Example 2
A 0.015 kg marble moving to the right at 0.225 m/s makes an elastic head-on
collision with a 0.03 kg shooter marble moving to the left at 0.18 m/s. After
the collision, the smaller marble moves to the left at 0.315 m/s.
Assume that neither marble rotates before or after the collision and that
both marbles are moving on a frictionless surface. What is the velocity of the
0.03 kg marble after the collision?
Given:
m1 = 0.015 kg
m2 = 0.030 kg
v1i = 0.225 m/s to the right, v1i = +0.225 m/s
v2i = 0.180 m/s to the left, v2i = –0.18 m/s
v1f = 0.315 m/s to the left, v1f = –0.315 m/s
Unknown: v2f = ?
𝑣2𝑓
𝑣2𝑓
𝑚1 𝑣1𝑖 + 𝑚2 𝑣2𝑖 − 𝑚1 𝑣1𝑓
=
𝑚2
(0.015)(0.225) + (0.03)(−0.18) − (0.015)(−0.315)
=
0.03
𝑣2𝑓 = 9 × 10−2 𝑚/𝑠 𝑡𝑜 𝑡ℎ𝑒 𝑟𝑖𝑔ℎ𝑡