[DOCUMENT TITLE]
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Do you know what makes objects move? Force is what
makes every object move. A force is a push or pull upon an
object resulting from the object's interaction with another
object. Based on Newton’s Second Law of Motion, applying
force to an object will cause the object to move or accelerate.
In more specific terms, Newton mentioned in this law that the
net force of an object is equal to the product of the object’s
mass and its acceleration.
Now, consider this scenario: two objects moving towards each other. What will happen
next? Of course, they’ll collide and will eventually there will be a change in their respective
motion. How is this so? Is force still an appealing factor in this situation? Or are there any other
considerations for this situation?
In this module, we will learn more about momentum and impulse. This module covers
two topics:
1. Describing Momentum & Impulse; and
2. Conservation of Momentum.
After going through this module, you are expected to:
1. relate impulse and momentum to collision of objects (e.g., vehicular collision)
(S9FE-IVb-36); and
2. Infer that the total momentum before and after collision is equal (S9FE-IVb-37).
Read, discover, and have fun!
Before you could proceed on the module, we must first assess what you already know
regarding projectile motion. Below is short pre-assessment for you to answer.
Direction: Read each question carefully and select the best answer/s accordingly. Write the letter
of your answer before the number.
____1. The momentum of an object is dependent upon an object’s ________ and ________.
a. size and shape
c. mass and velocity
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b. mass and speed
d. mass and energy
____2. Which of the following the unit of momentum?
a. kg ⋅ m/s
c. kg ⋅ J
2
b. kg ⋅ m/s
d. kg ⋅ J2
____3. A big fish swims upon and swallows a small fish at rest. After lunch, the big fish has less
a. momentum
c. velocity
b. mass
d. none of the above
____4. A 0.250 kg cart moving at 0.400 m/s has how much momentum?
a. 0.1 kg ⋅ m/s
c. 10 kg ⋅ m/s
b. 1 kg ⋅ m/s
d. 100 kg ⋅ m/s
____5. Which object listed below has the greatest momentum?
a. A 0.05 kg object rolling at 0.2 m/s.
c. A 0.15 kg object rolling at 2 m/s.
b. A 0.15 kg object rolling at 1 m/s.
d. A 0.4 kg object rolling at 2 m/s.
____6. A 2 kg cart has a momentum of 16 kg m/s. What is its velocity?
a. 8 m/s
c. 18 m/s
b. 0.125 m/s
d. 32 m/s
____7. The unit for Impulse is
a. N/s
c. N ⋅ s
b. N
d. s
____8. When the velocity of an object is doubled, its momentum
a. remains unchanged in accord with the c. quadruples
conservation of momentum.
b. doubles
d. decreases
____9. An egg is thrown at a wall and at a bed sheet. The force of impact will be
a. greater against the wall
c. equal
b. greater against the sheet
d. none of the above
____10. True or False: A big truck will always have more momentum than a small car.
a. True
b. False
Suppose you are doing something (let’s say you are studying or playing an online game)
and you are at the peak of your concentration. You are then in your momentum. However, your
mother asked you to stop whatever you are doing to buy something at the store. You become
annoyed, you lost your concentration and your momentum is gone. The same thing applies when
we talk about momentum of object in Physics (at least to some aspects).
How do we define momentum in Physics? What affects the momentum of objects? Let’s
do the activity below to find out.
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Activity
INVESTIGATING MOMENTUM
Objective:
Identify the factors that affect momentum.
Materials:
cardboard or folder at least 30 cm long, books, protractor, ruler, tape, and two
marbles of different sizes
Procedure:
1. Set up your piece of cardboard or paper folder to create a track like that of the picture
shown below. Make sure that the sides of the track are folded so that the marble would
not fall off when we do the activity. Label the distances of the track at 10 cm, 15 cm, 20
cm, and 25 cm.
Figure 1. track made from folder
2. Place several books on top of a table and position the track at an angle of about 15
degrees from the horizontal.
3. Using a paper folder/cardboard, create a little teepee hut just like what is shown below.
Figure 2. teepee hut made from paper folder
4. Attach the bottle cap on the arm using a double-sided tape. This is you catapult cup.
Now your catapult is ready.
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4. Place the little hut about 5 cm from the foot of the inclined plane. Label this as the little
hut’s initial position.
Figure 3. placement of the inclined plane and the hut
5. Let the marble roll from the 10 cm mark on the inclined plane. Measure how far the hut
moved. Record this as the stopping distance.
Stopping Distance (cm) of Stopping Distance (cm) of
Initial Distance (cm)
Small Marble
Large Marble
10
15
20
25
6. Repeat steps 4 and 5 while varying only the initial position/distance for 15 cm, 20 cm, and
25 cm.
7. Do steps 3 to 5, this time using the large marble. Record your data in the table above.
Guide Questions:
1. How will you compare their stopping distances?
2. What do you think happens to the velocity of the marbles as their point of release
increases?
3. Describe the stopping distance of the two marbles as their point of release increases.
4. If momentum is a measure of how difficult it is to stop a moving object, which of the two
marbles had a greater momentum at the same point of release?
5. How will it be possible for the two bodies of different masses to have equal momentum?
Consider this scenario: A car, with a mass of 1,500 kg, is travelling at a velocity of 80 kph
on a freeway. A truck, with a mass of 10,000 kg, and is also travelling at the same velocity at the
freeway. Suddenly, both of the vehicles lost their brakes and are about to crash onto a wall.
Which of two vehicles do you think will cause more damage to the wall? If the vehicles have equal
velocities, what factor contributed to the impact of collision?
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Figure 4. car and truck size comparison
Although the two vehicles possess the same velocities, they have different masses. Of
course, the truck has a greater mass that the car. And because the truck has a greater mass, its
damage to the wall will be far greater as compared to what the car will cause.
Let’s think of a new scenario. Let’s assume that two cars of the same model are travelling
on the road. Both of the cars have the same mass. However, one car is travelling on a flat road
while the other one is travelling downhill. If both of the cars lost their brakes and are about to
crash onto a wall, which of two do you think will cause more damage to the wall? This time, what
factor contributed to the impact of collision?
Figure 5. car on the left travels on a flat road while car on the right travels downhill
In this scenario, both of the cars have the same masses. Yet, they do have the same
momentum. Why is this so? If you think about it, the velocity of the cars contributes largely to
their momentum difference. Compared to car travelling on a flat road, a car going downhill has
a greater velocity. Also, the car travelling downhill will cause more damage to the wall that the
other car.
In your activity earlier, it was mentioned that momentum is a measure of how difficult it
is to stop a moving object. That is because an object’s momentum is also known as inertia in
motion. Inertia, as we know it and as stated in Newton’s First Law of Motion, is the natural
tendency of an object to resist changes in its motion. Now, which do you think has a greater
momentum, a light object or a heavy one? A slow object or a fast one?
Momentum depends on two factors – mass and velocity. For objects moving at the same
velocity, a more massive object has a greater inertia in motion, thus, it has a greater momentum.
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For objects having the same mass, a faster moving object has a greater inertia in motion, and
also, has a greater momentum.
The larger the mass of an object is, the greater is its momentum (vice versa).
The faster an object moves, the greater is its momentum (vice versa).
Again, momentum considers the mass and velocity of objects. Operationally, momentum
is defined as the product of mass and velocity of an object.
p = mv
where p = momentum (kg ⋅ m/s), m = mass (kg), and v = velocity (m/s)
Let us try applying the formula above.
Example 1. Vanessa Carlton is making her way downtown, walking fast, faces pass and until she’s
homebound. What is her momentum while riding her piano downtown if she travelled with a
velocity of 3 m/s and she weighs 55 kg?
Solution:
p = mv
p = (55 kg) (3 m/s)
p = 165 kg ⋅ m/s
Given:
v = 3 m/s
m = 55 kg
p=?
Remember this:
Equation to Use
𝑝
𝑚=
𝑣
𝑝
𝑣=
𝑚
If you are looking for…
If you know…
mass
momentum and velocity
velocity
momentum and mass
Activity
SOLVING MOMENTUM
Complete the table below.
Object
Mass (kg)
Velocity (m/s)
Momentum
(kg⋅m/s)
Bird
Yacht
Bullet
Sloth
Sleeping Pig
0.03
18
5 m/s
600
30,000,000
0.004
6 kg
200 kg
3.24
at rest
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Now that you understood what momentum is, let us proceed to another topic. Let us talk
about change in momentum.
Figure 6. getting hit by a ball versus catching a ball
Have you experienced getting hit by a ball? It hurts, right? But if we try catching the ball,
would it still hurt? Getting hit by a ball and catching the ball both involve contact between bodies
and change in momentum. However, one has a greater change in momentum than the other. So,
which of the two experiences is it?
Let’s try another situation. You are to throw an egg to a wall and another egg to a heap
of pillows. Which will break the egg, the wall or the pillows? Using our common sense, the answer
is the wall. This is because when the (egg’s) motion is abruptly stopped, its momentum suddenly
changes. Meanwhile, the egg is likely not to break when thrown over a heap of pillows. That is
because when we increase the time of impact, we can lesson the force of impact.
In physics, an external force acting on an object over a specific time leads to a change
in momentum of the object. The change in momentum is called IMPULSE. Impulse can be
written mathematically as:
I = Ft
where I = impulse (N ⋅ s), F = force (N), and t =time (s)
Otherwise, it can be written mathematically as:
I = mvf - mvi
where I = impulse (kg ⋅ m/s), m = mass (kg), vf = final velocity (m/s), and vi = initial velocity
(m/s)
Also, remember this:
Equation to Use
𝐼
𝐹=
𝑡
𝐼
𝑡=
𝐹
If you are looking for…
If you know…
force
impulse and time
time
impulse and force
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Example 2. What is the change of momentum of a baseball struck with a force of 50 N in 0.5 s?
Given:
F = 50 N
t = 0.5 s
I=?
Solution:
I = Ft
I = (50 N) (0.5 s)
I = 25 N ⋅ s
Example 3. A 5.0 newton force impacts an impulse of 15 Newton-seconds to an object. The force
acted on the object for a period of ___________.
Given:
F = 5.0 N
I = 15 N ⋅ s
t=?
Solution:
𝐼
𝐹
15 𝑁 ⋅ 𝑠
𝑡=
5.0 𝑁
t=3s
𝑡=
Activity
SOLVING IMPULSE
Solve the problems below.
1. A net force of 12 N acting north on an object for 4.0 s will produce an impulse of
_______.
2. A force of 10. N acts on an object for 0.010 s. What force, acting on the object for
0.050 s, would produce the same impulse? ________
Figure 7. billiards exhibiting collision
In a billiard game, we use the cue stick to strike
the cue ball (the white ball) which will then strike the
billiard balls. As we strike the cue ball, the cue ball
gains momentum. Now that the cue ball gained
momentum, what will happen to its momentum if it
struck the billiard balls? Will there be a change in the
momentum of the cue ball and the billiard balls? Will
there be change of momentum in this system?
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Let us define first what is a system. A system, as it is defined in physics or chemistry, is
nothing more than a collection of objects (or smaller systems) that can be identified. This object
or objects are our focus of study or investigation.
What is the law of conservation of momentum all about? Conservation of momentum, a
general law of physics, states that the momentum never changes in an isolated collection of
objects; that is, the total momentum of a system remains constant. That means though the
individual momentum of objects may change, the total momentum of the system will remain as
it is. In our example earlier, the cue ball gained its momentum however lost a portion of it when
it struck the billiard balls. The lost momentum by the cue ball is then gained by the billiard balls.
In this sense, the momentum is not lost but only transferred from one object to another. Thus,
momentum is conserved.
Figure 8. how do you think momentum is conserved in this situation?
Moreover, the law of conservation of momentum can be interpreted as
pinitial = pfinal
total initial momentum = total final momentum
or
m1v1 = m2v2
where m1 = mass of object 1, v1 = velocity of object 1, m2 = mass of object 2, and v2 =
velocity of object 2
Let us try applying the formula from above.
Example 4. A couple of ice skaters stand together. They “push off” and travel directly away from
each other – the boy with a velocity of 0.50 m/s and the girl with a velocity of 0.65 m/s. If the
mass of the boy is 60.0 kg, what is the girl’s mass? Neglect friction.
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Given:
Suppose object 1 is the boy and
object 2 is the girl.
m1 = 60.0 kg
v1 = 0.50 m/s
v2 = 0.65 m/s
m2 = ?
Solution:
m1v1 = m2v2
𝑚1 𝑣1
= 𝑚2
𝑣2
𝑚
(60.0 𝑘𝑔)(0.50 )
𝑠 =𝑚
2
0.65 𝑚/𝑠
𝑚
30.00 𝑘𝑔 𝑠
= 𝑚2
0.65 𝑚/𝑠
𝑚
46.15 = 𝑚2
𝑠
Remember this:
Equation to Use
If you are looking for…
𝑚1 𝑣1
= 𝑚2
𝑣2
mass of second object
𝑚1 𝑣1
= 𝑣2
𝑚2
velocity of second object
If you know…
mass and velocity of first
object and velocity of second
object
mass and velocity of first
object and mass of second
object
Activity
APPLYING LAW OF CONSERVATION
Solve the problem below.
There are cars with masses 4 kg and 10 kg respectively that are at rest. A car having the
mass 10 kg moves towards the east with a velocity of 5 m/s. Find the velocity of the car
with mass 4 kg with respect to ground.
Since we’re already talking about conservation of momentum, let’s also talk about
collision. A collision is an encounter between objects resulting in exchange of impulse and
momentum. Because the time of impact is usually small, the impulse provided by external forces
like friction during this time is negligible. If we take the colliding bodies as one system, the
momentum is therefore approximately conserved.
total momentum before collision = total momentum after collision
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There are two types of collision: elastic collision and inelastic collision.
1. Elastic Collision – one in which the total kinetic energy of the system does not change
and the colliding objects bounce off after the collision.
2. Inelastic Collision – one in which the total kinetic energy of the system changes (that is,
it can be converted to some other form of energy). Objects that stick together after
collision is said to be perfectly inelastic.
Figure 9. (a) billiards is an example of elastic collision while (b) football is an example of inelastic collision
Activity
IDENTIFYING TYPES OF COLLISION
Identify the type of collision shown on the situations below. Write EC if it is an elastic
collision. Otherwise, write IC if it is an inelastic collision.
1. two cars crashed onto each other
2. two spinning toy tops colliding
3. two rams ramming each other
4. baseball struck by a batter
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A. Multiple Choice. Choose the letter of the best answer. Write your answer on the space
provided.
____1. An object’s momentum can be calculated by multiplying the velocity of the object by its
___________.
a. time
c. acceleration
b. mass
d. length
2-6. For each item, determine the object with a greater momentum.
____2.
a. 30 g marble rolling at 0.2 m/s
b. 2 kg bowling ball at rest
____3.
a. 2,500 kg pig running at 3 m/s
b. 0.025 kg bullet shot at 100 m/s
____4.
a. 75-kg sprinting man
b. 75-kg walking man
____5.
a. 35 kg child running at 2 m/s
b. 25 kg child running at 2.5 m/s
____6.
a. 101 kg cow moving at 4 m/s
b. 110 kg carabao moving at 3 m/s
____7. What is true about impulse and momentum?
a. Impulse deals with velocity while momentum deals with change in velocity.
b. Impulse is mass times velocity while momentum is force times time.
c. Momentum is the mass of a substance multiplied by the velocity while impulse is just the
change of momentum.
d. Momentum and impulse are unrelated to each other.
____8. When a golf club hits a golf ball, the change in momentum of the club is ______ the change
in momentum of the ball.
a. less than
c. equal to
b. greater than
d. none of the above
____9. A baseball was struck by a bat with a force of 50 Newtons for 0.25 seconds. What is the
impulse of the baseball?
a. less than 12.5
c. equal to 12.5
b. greater than 12.5
d. none of the above
____10. In a perfectly inelastic collision, a ball dropped from a certain height would
a. bounce at a greater height
c. bounce at a lesser height
b. bounce at the same height
d. would stick to the floor
B. Problem Solving. Solve the problem below and show your solutions. Put your final answer in
a box and do not forget to include its unit.
A ten-year-old boy (26 kg) sits on a wheeled office chair (16 kg)
holding a fire extinguisher (18 kg when empty). He points the
discharge horn to the right and ejects 9 kg of carbon dioxide at 20
m/s. What is his speed and direction after the fire extinguisher is
emptied (assuming friction is negligible)?