So let us look at an example where we apply the principle of impulse and momentum.
Now, what I've drawn here is a crate that moves along a floor while a force of F is 600.
Newton is applied the crate as a mass of 80 kilograms of retinoic, efficient of friction.
But for simplicity, let's ignore the coefficient of friction.
I will tell you what you should do when you have sufficient or friction, but let's just ignore it for
now.
And the question is, if the crate is initially stationary, the term, the speed of the 20s, 10 seconds.
So immediately, because time is mentioned here, these 10 seconds, that points to the fact that we
need to use the principle of impulse and momentum to solve this problem.
So let us write down the principle of impulse momentum, so M one, V one vector, plus I the impulse
vector form is MTV to vector on the right and side.
I have drawn my coordinate axis and I've chosen X to be in the horizontal direction and Y to be in the
vertical direction.
We're only going to have movement in the X direction because the forces only applied in the X direction.
I can therefore simplify my vector equation by writing in one V one in the X direction.
Plus the impulse in the X direction is aimed to to in the X direction.
So let's plug in our values.
M1, that's the mass is 80 kilograms, and I've said that the grade was initially stationary, so V1
one is zero plus the impulse.
How do we calculate the impulse?
That's the force multiplied by the time.
So that's six hundred multiplied by ten is equal to 80 multiplied by V2.
And now it's simple to solve for V two, which is Civita that is six thousand divided by eight and that
gives us seventy five meters per second in the X direction.
So if we did not neglect the effects of friction, we would have had an impulse created by friction
because friction is in the opposite direction of movement.
So we would have had a negative impulse.
So we would have gone and we would have calculated the frictional force.
And as we know, that's the frictional coefficient multiplied by the normal force.
So we would have taken the mass of the great multiplied by nine point eight to one that would give us
the weight of the great.
That would be the normal force.
We would multiply that by the frictional coefficient and then we would get a frictional force that would
work and the opposite direction of movement.
So that would be the negative X direction.
And so on our impulse and momentum equation, we would have had in one V, one X plus the sum of the
impulses.
So we would have had the positive impulse of the force that would be six hundred multiplied by ten seconds,
and we would have the negative impulse of the friction and that would be the frictional force also multiplied
by ten seconds, because that's the time that it works in on the crate would be into V to X and then
we would have gotten a smaller velocity for V2.
So if you understand that, then you understand the concept of impulse and momentum.
What about a case like this where the force is not applied in the horizontal direction, but with an
angle to the horizontal?
Now there is a force that as a component in the X direction and the wind direction.
So that means this force has an impulse in the X and the Y direction, note that that doesn't mean that
the great will also move in the direction.
That will depend on whether the weight of the crate is larger than the Y component of the force, if
the weight of the crate is larger than the Y component of the force, then the crate won't be picked
up from the ground.
It will then just move in the X direction.
And so then we would only have a X component of the velocity, but if the Y component of the force is
larger than the weight of a crate, then the crate would move in the direction that we need to apply
the equation of impulse and momentum in the X and the Y directions.
And so when we look at the principle of work and energy, then work is only applied when the credit
moves in the direction of the force.
So for this example, there won't be any work in the Y direction unless the credit moves in the right
direction.
But impulse?
Doesn't necessarily cause movement, and therefore you can have an impulse, even if the crowd does
not move in that direction.