Introduction to Impulse & Momentum - Physics
Summary
TLDRThis educational video delves into the concepts of impulse and momentum in physics. Momentum is defined as mass times velocity, indicating mass in motion. It's a vector quantity with both magnitude and direction. The video explains how to calculate momentum with examples, including direction considerations. Impulse, the integral of force over time, is also explored, along with the Impulse-Momentum Theorem. The theorem links impulse to changes in an object's momentum and is used to calculate final velocities and momenta with a practical example involving a force applied to a block.
Takeaways
- 📚 Momentum is defined as the product of an object's mass and velocity.
- 🚄 Objects in motion possess momentum; a train has significant momentum due to its large mass, while a sports car has momentum due to its high velocity.
- ✈️ An object at rest, like an airplane, has zero momentum because it is not moving.
- 📏 Momentum is a vector quantity, possessing both magnitude and direction, derived from the scalar mass and vector velocity.
- 🔢 The units of momentum are typically kilograms times meters per second (kg·m/s).
- 📉 The direction of an object's momentum aligns with its direction of motion; rightward motion is positive, and leftward is negative.
- 💥 Impulse is calculated as the product of force and the time over which it acts, with units of newtons times seconds (N·s).
- 🔄 The impulse-momentum theorem states that the impulse applied to an object is equal to the change in its momentum.
- 📉 Force can be defined as the rate of change of an object's momentum over time, mathematically expressed as (Δp / Δt).
- 📐 Newton's second law connects force, mass, and acceleration, where the net force on an object equals its mass times acceleration.
Q & A
What is momentum?
-Momentum is a vector quantity that represents the mass of an object in motion, calculated by multiplying the object's mass by its velocity.
What is the formula for calculating momentum?
-The formula for calculating momentum is given by p = mv, where p represents momentum, m is the mass, and v is the velocity of the object.
Why is momentum considered a vector quantity?
-Momentum is considered a vector quantity because when you multiply a scalar (mass) by a vector (velocity), the result is a vector that has both magnitude and direction.
What are the units of momentum in physics?
-In physics, the units of momentum are typically kilograms times meters per second (kg·m/s).
How do you determine the sign of momentum?
-The sign of momentum is determined by the direction of the object's motion. If it's moving to the right (or east), the momentum is positive, and if it's moving to the left (or west), the momentum is negative.
What is impulse in physics?
-Impulse in physics is the product of the force applied to an object and the time for which the force is applied, represented by the formula J = Ft, where J is impulse, F is force, and t is time.
What is the relationship between impulse and momentum?
-According to the impulse-momentum theorem, the impulse applied to an object is equal to the change in the object's momentum, expressed as J = Δp.
What does the impulse-momentum theorem tell us about force?
-The impulse-momentum theorem tells us that force is the rate at which the momentum of an object changes, which can be expressed as F = Δp/Δt.
How is impulse related to Newton's second law?
-Impulse is related to Newton's second law through the concept that the net force acting on an object is equal to the mass of the object times its acceleration, which can also be viewed as the rate of change of momentum.
Can you provide an example of calculating impulse and change in momentum from the script?
-Yes, in the example provided, a force of 200 newtons is applied for 5 seconds to a 50 kg block initially moving at 10 m/s east. The impulse is calculated as 200 N × 5 s = 1000 N·s. The change in momentum is also 1000 kg·m/s, assuming the force is in the same direction as the initial velocity.
What is the final velocity of the object in the example problem if the force increases its momentum?
-In the example, the final velocity is calculated by adding the change in velocity to the initial velocity: v_f = v_i + Δv = 10 m/s + 20 m/s = 30 m/s.
How is the final momentum of the object calculated in the example?
-The final momentum is calculated by multiplying the final velocity by the mass of the object: p_f = m × v_f = 50 kg × 30 m/s = 1500 kg·m/s.
Outlines
🚀 Understanding Momentum
This paragraph introduces the concept of momentum in physics, emphasizing its relationship with mass and velocity. Momentum, represented by the lowercase 'p', is defined as the product of an object's mass and its velocity, indicating the quantity of motion. The paragraph explains that any moving object possesses momentum and uses examples such as a train and a sports car to illustrate this point. It also clarifies that while mass is a scalar, velocity is a vector, and thus the product results in a vector quantity for momentum, which includes both magnitude and direction. The units for momentum are discussed, typically kilograms times meters per second. An example is provided to calculate the momentum of a 10 kg block moving at 5 m/s to the east, resulting in a momentum of 50 kg*m/s to the east. The paragraph also covers how to determine the sign of momentum based on the direction of motion.
🔧 Impulse and Its Relation to Momentum
The second paragraph delves into the concept of impulse, defined as the product of force and the time over which it is applied. It contrasts impulse with momentum, noting that while both have units of newton-seconds, they represent different physical quantities. The Impulse-Momentum Theorem is introduced, stating that the impulse applied to an object is equal to the change in its momentum. The paragraph then explores the relationship between force, momentum change, and time, leading to the definition of force as the rate of change of momentum. An example problem is presented where a 50 kg block is subjected to a 200 N force for 5 seconds, and the viewer is prompted to calculate the impulse, the change in momentum, and the final momentum and velocity of the block. The paragraph concludes with a teaser for additional resources on related topics and an encouragement to subscribe to the channel for more content.
📚 Calculating Impulse and Momentum
The final paragraph provides a step-by-step calculation for the example problem introduced in the previous section. It starts by calculating the impulse as the force of 200 N applied over 5 seconds, resulting in 1000 N*s. The change in momentum is then determined by applying the Impulse-Momentum Theorem, which equates the impulse to the change in momentum. The paragraph explains that since the force and velocity are in the same direction, the force increases the object's momentum, making the change positive. The calculation proceeds to find the final velocity by dividing the change in momentum by the object's mass and then adding the initial velocity, resulting in a final velocity of 30 m/s. Lastly, the final momentum is calculated by multiplying the object's mass by its final velocity, yielding 1500 kg*m/s. The paragraph concludes with a summary of the key points about impulse and momentum and an encouragement to explore further resources and subscribe to the channel.
Mindmap
Keywords
💡Momentum
💡Mass
💡Velocity
💡Scalar
💡Vector
💡Impulse
💡Force
💡Impulse-Momentum Theorem
💡Units
💡Acceleration
💡Newton's Second Law
Highlights
Momentum is defined as mass times velocity.
Momentum represents mass in motion.
An object at rest has no momentum.
Momentum is a vector quantity with both magnitude and direction.
The unit for momentum is kilograms times meters per second.
Momentum is positive if an object moves to the right and negative if it moves to the left.
Impulse is defined as force multiplied by time.
Impulse has units of newtons times seconds, equivalent to momentum units.
The impulse-momentum theorem states that impulse equals the change in momentum.
Force is the rate at which momentum changes, defined as delta p over delta t.
Newton's second law relates force to mass and acceleration.
An example problem involves calculating impulse, change in momentum, and final momentum and velocity.
Impulse can be calculated by multiplying force by the time the force is applied.
The direction of force and velocity determines whether the change in momentum is positive or negative.
The change in momentum can be found using the impulse-momentum theorem.
Final momentum is calculated by adding the change in momentum to the initial momentum.
Final velocity is calculated by adding the change in velocity to the initial velocity.
The video provides additional resources for further study on impulse, momentum, and collisions.
Transcripts
in this video we're going to talk about
impulse
and momentum
but let's begin our discussion
with momentum
what is momentum
i know you heard of this word but
what really is it
here's the formula for momentum
momentum represented by the lowercase p
symbol
is mass
times velocity
now let's think about what that means
momentum is basically mass in motion
any object that is moving has momentum
a train for example
that's moving has a lot of momentum
because it has a lot of mass
a sports car which may not have as much
mass but it's moving fast also has a lot
of momentum
an airplane at rest has no momentum
because it's not moving so momentum is
basically
mass
in motion
now is momentum a scalar quantity
or a vector quantity what would you say
mass
is a scalar quantity
and velocity
is a vector quantity
if you recall the vectors have both
magnitude and direction
there's no direction of mass
now what happens
when we multiply a scalar by a vector
a scalar times a vector will give you
another vector
that vector could be
greater or smaller in magnitude but it
will give you another vector
so momentum
is a vector
it has both magnitude
and direction
now let's talk about the units of
momentum
in physics mass is typically in
kilograms
velocity is usually in meters per second
so momentum will have the units
kilograms
times meters per second
at least this is
the most common unit that you'll see for
momentum
now let's work on an example problem
let's say we have
a 10 kilogram block
sliding along a horizontal frictionless
surface
at a speed of 5 meters per second east
so the speed is 5 meters per second but
the velocity is 5 meters per second east
what is the momentum of the block
well momentum is mass times velocity
so the mass is 10 kilograms the velocity
is 5 meters per second east
so the momentum will be positive
50
kilograms times meters per second
the reason why it's positive
is because
the object is moving to the right
now what if the object was moving to the
left
so let's say we have
a 20 kilogram object
at three meters per second to the left
what is the momentum
well momentum is mass times velocity
the mass
is 20 kilograms
and what is the velocity
is it positive or negative three meters
per second
because the block is moving to the west
to the negative x direction the velocity
is negative
so it's negative three meters per second
which means the momentum is negative 60
kilograms times meters per second
so when dealing with momentum if you
have an object that's moving to the
right the momentum should be positive
if it's moving to the left
the momentum should be negative
now let's talk about impulse
what is impulse
in physics
impulse is force
multiplied by time
now be careful because sometimes you'll
see i which may represent inertia in
physics
but in this example i'm using i as
impulse
so it's force multiplied by time
unit for force is the newton
and for time it's typically in seconds
so impulse
will have the units
newtons
times seconds
there's something known as the impulse
momentum theorem
according to the impulse momentum
theorem
the impulse is equal to the change in
the momentum of the object
so a force
acting on an object for a given time
interval is equal to the mass
times the change in the velocity of the
object
so this
is the impulse momentum theorem
now
we know the unit for impulse is newton's
time seconds
and the unit for momentum
is kilograms
times meters per second
so these units are equivalent
but when you see newton's times seconds
typically it corresponds to impulse and
if you see kilograms times meters per
second
that usually corresponds to momentum
but those units they're equivalent
though
now there is an important point to
mention regarding impulse and momentum
so we said that impulse is equal to the
change in momentum
and impulse
is equal to force
multiplied by time or the change in time
or the time that the force has been
acting on the object for
now if we divide both sides by delta t
we get something interesting
and that is
the true definition of a force
so a force is really
the rate at which the momentum of the
object changes
its delta p over delta t
so if you know how fast the momentum of
the object is changing
you basically know the net force acting
on that object and so this is another
way in which you could define a force
in physics
now this equation is related to newton's
second law momentum is mass
times the change in velocity
and what do you know about the change in
velocity over the change in time
so that is a v final minus v initial
divided by t
this is equal to the acceleration
the acceleration of the object or of any
object rather it's the rate at which the
velocity changes
and so what we could do is replace
delta v over delta t with acceleration
and so we get mass times acceleration
and so according to newton's second law
the net force acting on an object is
equal to the mass of the object times
the acceleration of the object and it's
related to this expression
a force acting on an object is equal to
the rate at which the momentum changes
for that object
now let's work on an example problem
so here we have a horizontal
frictionless surface
and
we have a block
with a mass of 50 kilograms
and we're going to apply a force
of 200 newtons
on this block
and we're only going to apply this force
for a specific time period
and that is
that force will be active on this object
for only five seconds
and now let's say that before the force
was
before the force acted on the object
let's say that the initial velocity
of the object is 10 meters per second
east
so i want you to find a few things
calculate the impulse
acting on the object
and then part b
calculate the change and momentum of the
object
part c
calculate the final momentum of the
object
and then part d
calculate the final velocity
of the object so using the formulas that
we talked about see if you can calculate
these things
feel free to pause the video
if you want to
now before we get started on this
problem
i want to mention a few things
that is first of all for those of you
who want more problems on impulse
momentum
elastic collisions inelastic collisions
conservation of momentum and stuff like
that
check out the links in the description
section below i'm going to post some
more videos on those topics
and whatever you do
don't forget to subscribe to this
channel
if of course you like this video
so let's go ahead and begin
how can we calculate the impulse
acting on this object
the impulse is simply
the force
multiplied by the time in which the
force is active
so it's 200 newtons
multiplied by 5 seconds
so that gives us i'm going to write the
answer here
1000
newtons
times seconds
so that's part a
now part b what is the change in the
momentum
according to the impulse momentum
theorem the impulse is equal to the
change in momentum
now here's a question for you
is the force
increasing the momentum of the object or
decreasing the momentum of the object
notice that the force vector and the
velocity vector are in the same
direction
so therefore the force is accelerating
the object it's making it move faster
therefore it's going to increase the
momentum
so the change in momentum is positive
because it could be negative
this could be negative one thousand
instead of positive one thousand
another way in which you could look at
this is that
the force is a vector and it's directed
to the right so it has to be positive
which means the impulse is positive
and so the momentum is going to be
positive so it's a thousand kilograms
times meters per second but i'm out of
space so
i didn't write it there now let's
calculate the final momentum
so we know that the change of momentum
is the mass
times the change in velocity
and the change in velocity
is the final velocity minus the initial
velocity
and delta p is a thousand
now we have
a block with a mass of 50 kilograms
the initial speed is 10
and so we can get the answer
let's begin by dividing both sides by
50.
and so a thousand
divided by 50 that's the same as 100
divided by 5 which is 20.
and now all we need to do
is add 10 to both sides
well that will give us the final
velocity which is part d so i might as
well write that answer now
so the final velocity is 30.
i need to calculate the final momentum
which
i could just use this formula the final
momentum is simply the mass times the
final velocity
so we have a mass of 50
and a final velocity of 30 meters per
second
and so if we multiply 5 times 3
that's 15
and then add in the two zeros that gives
us 1500
so it's 1500 kilograms
times meters per second
so now i'm gonna stop the video here
and uh hopefully it gave you a decent
understanding of impulse and momentum
and how they're related
so thanks again for watching and don't
forget to check out the links below and
subscribe to this channel
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