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We are doing Physics, Momentum Problems
Today we are doing problems concerning two colliding cars
first problem is with
one car moving at eighty Kilometers as per hour toward
another stationary car and they're gonna
couple, meet and touch each other and then we're gonna see
how fast both of them afterwards are going
so first thing we do
is we need to use the equation m times v
is mass times velocity equal momentum
so the momentum of this car
right here since the mass is
Let's just say the mas is x and the mass of this is x because they are identical
so it will be x
times eighty and then this would be
plus let's say this one is x as well
the velocity of this one is zero so zero X
equals now the combined mass
once they are colliding so it will be two x times
v We are looking for this v right here
so now what we do now is we know that eighty
x equals
two x v so that means
that v
equals 40
kilometers per
hour yeah
Okay, so next for part b we have to find
the velocity of the carts after they collide
cart one is moving at 100 kilometers per hour
cart two is moving at 80 kilometers per hour
and we are looking for their velocity after they collide
So since our masses are identical we can just use that as x
The velocity of the first cart is 100
plus the mass of the second cart which is x
times the velocity which is 80 and that's equal to
oh, sorry
negative 80 because they're traveling in opposite directions
The negative is important
2 x is your mass times the velocity
after they collide and
then you solve that by adding them together
180 x (Negative 80 so it will just be 20 x)
Sorry, there's a negative so 20 x
as Vicki says the negative it is important yes
20 x and then
That is equal to 2 x times v
20 x divided by 2 x 10
equals v
(10 kilometers per hour going in which direction?)
per hour moving
towards the right
in the positive direction Positive
So in this problem we have one cart going 80 kilometers per hour
and the other car going 100 kilometers per hour in the same direction
and they're going to hit each other and its an inelastic collision
because stick together and they won't bounce off
So what we're trying to find is how fast they're going after the collision the whole carts together
So we have our equation here the first mass of the first cart
is x because it's not relevant to this problem so we will us it as an x
X times the velocity of that cart which is 80 kilometers per hour
plus the mass of the second cart which is also x
times the velocity of the second cart which is hundred kilometers per hour
equals the combined mass
of both carts X plus x is 2 x
times the velocity of the entire system which is what we are solving for
So we put it as v So we have 80 x plus 100 x
equals
2 x v
add these together it becomes
80 x equals 2 x v
So we solve for v which is the velocity of the entire system after the collision
divide 180 X by 12 X
so that leaves us with 90 equals the final velocity
beautiful