Newton's third law states that every action has an equal and opposite reaction.
It is important to recall how impulse is connected to momentum with the F component.
So when two cars collide, the forces are the same and opposite.
If the forces are the same and opposite then their momentums are the same because of F.
If the forces and momentum are the same, then their impulses are equal since change in m=J.
The only thing that is different is the acceleration.
F=ma
The truck has a big mass
Truck= F = Ma
Car= F = mA
if the car has a small mass, then the acceleration is going to be bigger. (Newton's second law)
momentum is mass times velocity
mass is usually constant, so velocity can sometimes change. Remember that velocity can change because any change in velocity is acceleration. So that is why we have change in momentum.
Change in momentum equals impulse. Now impulse equals force times the change in time. How are these two connected? Well remember that velocity can change? And that this change is called acceleration? Acceleration requires a force, and that is where we get the F in impulse's equation.
p=mv
change in p= J
J= F x change in t
Why do air bags keep us safe?
When you are driving in a car and you crash, you go from moving to not moving. Remember that momentum is p= mass x velocity.
However the change in momentum equals pfinal- pinitial. This is the part I was talking about. You are going from moving to not moving. Now matter how you are stopped, you will go from moving to not moving, so the change in momentum will always be the same. If the change in momentum is the same and since change in momentum = impulse, then impulse will always be the same. The airbag increases the change in time. Remember that J= F x change in time. Therefore if the change in time is increased then the force is decreased because impulse is constant. Then the force on you is decreased and you will have less of an injury.
p=mv
change in p= pfinal-pinitial
change in p= J
J= F X change in time
Now... for the change in momentum:
a car with a mass of 1000 kg starts form rest and gets up to a speed of 100m/s. what is the impulse?
change in momentum = pfinal-pinitial.
What we haven't said is that pfinal= mvfinal
and pinitial= mv initial.
SO
1000 (100)- 1000 (0)
SO the change in p = 100,000 kg m/s
or J= 100,000 Ns
Incorporating Impulse into this problem we add a change in time
So.. if the car was moving for 10 seconds what was the F needed to cause that same change in momentum?
J= F x change in t
Change in t= 10s
J= 100,000 Ns
so... 100,000 Ns/ 10s = 10,000 N
10,000 N= F
What if we had two cars? and what if we wanted to know what their velocity was after they collided?
Ptotalbefore = Ptotal after
Ma Va+ Mbvb= Ma+b x (Vab)
solve for Vab
you have to add the momentums together and the masses together to get the speed
this equation is actually just the same version as p=mv
but p you are adding the momentums, m you are adding the masses, and V includes both velocities.
You know how momentum is when something starts and stops? Well when I ball bounces, it is starting and stopping... but then starting again. This requires 2 impulses. An impulse to stop... and an impulse to start up back again. Remember how impulse equals F X change in time? Since force is needed in impulses, then that means you have 2x the force since you have two impulses. If you have 2x the force, then if a ball hits you and bounces off it will hurt more than if it hit you and stopped. Same with bullets. This is why cops have bullet proof vests that stop the bullet rather than make it bounce off them.
We've talked about impulse/momentum and their relationships. We've talked about the change in momentum. Now lets talk about conservation of momentum.
There was a question on a quiz that said to prove that momentum is conserved.
one example is from the lab when one cart was moving at a cart sitting still. The moving cart might have 8N and the cart at rest has 0 N. When they collide and move together, they have 8N. This is how momentum is conserved. Now the question asked us to prove newton's third law.
the equation was y=2.9333+ .3778
If Cart A has a mass of 2kg... and Cart B has a mass of 1kg... 2+1= 3
you can rule out .3778 because it is so close to zero
here are the steps:
write out the equation of the line (which we just did)
fill in the y axis units...
remember that equation we did before?
Ptotal before= Ptotal after?
MaVa + MbVb= Ma+b (Vab)
when the carts collide we are adding their masses and velocities together like we said. so that is why we have to add 2+1 like we said
basically when we translate the equation from y intercept to the mava one.. we get that y= p total before
and x is the VAB
and the 2.93 is the masses added together
because that's the same equation right?
ptotal before= total mass (total velocity)
MaVa+ MbVb= total mass (total velocity) + over here would be the .3778 but its too close to zero..
these are the separate cars= and you are adding them together
we compare the 2+1 to the 2.93 and we can comfirm newton's law.
Show how the conservation of momentum is derived from Newton's 3rd law+
Fa= -Fb
(all reactions have an equal but opposite reaction) (forces are equal but opposite)
there are forces in impulses
so...
Fa x change in time= -Fb x change in time
so..
Ja= -Jb
so since J equals the change in momentum..
change in Pa= -change in Pb
if you add -change in Pb to the other side it equals zero
so no total chnge in momentum of the system
or no net change
so momentum is conserved.
we just went from newtons 3rd law regarding force and since forces are needed for impulse we added impulse to the equation and since impulse is equal to the change in momentum, we added momentum. From there we can say that momentum is conserved.
Okay enough of momentum.
Let talk about the universal gravitation equation.
F= G m1xm2/ d squared.
BIG QUESTION: why is the moon responsible for the tides if the sun exerts a larger force on the two sides of the earth than the moon does?
It is the difference between the forces exerted on side A and side B from the sun that are less than the difference in the forces exerted on side A and B from the moon.
So what do we know?
everything with a mass is attracted to all other things with a mass
force is direction proportional to masss
force is indirectly proportional to distance
the less distance you have from the center of the Earth, the greater the FFORCE
F= G x m1xm2/dsquared
F= weight
G= universal gravitational force
m1= earth mass
m2= your mass
dsquared= distance between you and earth
Earlier we calculated weight by doing w=m(g)
and from there we find acceleration
a= fnet/m
Now since we find weight using the ug equation
and weight equals fnet in the acceleration equation, we can compare w and F to see if you get close to your weight and your actual weight(gravitational equation)
Here is a video explaining tides:
This video shows how tides are formed from the interactions of both the sun and the moon. We know this to be true from the universal gravitation equation. That force is inversely proportionate to distance, and even though the suns mass is larger and therefore has more force on the moon, the difference in these forces of side A and side B are less than the difference of forces on side A and side B of earth and moon.
This unit seemed to be a bit jumbled. Connecting tides with momentum..? Yeah I wasn't sure how to approach that one. I feel like I was a bit more on top of things this unit than last unit. I hope that next semester with a fresh start I can reorganize my thoughts. I did not have trouble processing and learning this time around like I did last time.. so that was good. I really enjoyed learning about this unit and making the connections that I could in this blog.
