Topic 3D: Momentum. Momentum considers speed and mass. A bowling ball and a baseball can have the same momentum. How?. A small fast mass can have the same momentum as a large slow object. Review: Can a bowling ball and baseball have the same inertia?. No, inertia means mass.
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A bowling ball and a baseball can have the same momentum. How?
A small fast mass can have the same momentum as a large slow object.
Review: Can a bowling ball and baseball have the same inertia?
No, inertia means mass
Momentum = mass x velocity
In equation format:
p= m x v
Momentum is assigned the variable p in equations because this concept used to be referred to as “persistence”. It never changed because m is already taken for mass.
Units kg m/s
An object with a mass of 1 kg and a velocity of 5 m/s has the same momentum as an object with a mass of 5kg moving 1m/s or 2 kg at 2.5 m/s, etc…….
A force
How can we change an object’s momentum?
When a force acts on an object, it causes an acceleration .
Fnet =ma
Also can be stated: When a force acts on an object, it changes the velocity of the object.
The amount of time the force acts determines the change in velocity
What is the relationship between Force (F) and time (t)?
Inverse
Rearrange the above to:
Force acting for time is known as IMPULSE (J)
Mass times velocity is known as MOMENTUM (p)
Momentum: p=m x ∆v
Impulse: J = F x t = ∆p
An impulse (F x t) causes a corresponding change in momentum (m x ∆v).
* J = Ft = mΔv= m(vf-vi)=Δp *
Force is the time rate of change of momentum
* J = Ft = mΔv=m(vf-vi)=Δp*
Time and force have an inverse relationship.
F x t = ∆ p F x t= ∆ p
For any given momentum change a large time will equal less damage (Force)This is the idea behind air bags, bouncy castles and egg catching. Increase the time for the change in velocity in a way that considers the mass.
Which is the safest stop?
What does this equation show us?
Forces and car crashes
F x t = ∆ p F x t= ∆ p
The change in momentum is the same. The force and time are different. And the “pain” felt is different.
These equations are split up on the reference table.
Next topic
Here it is all connected
* J = Ft = mΔv =Δp *
A Newton-second and a kilogram m/s are the same.
Newton-second is a kg (m/s2) x s = kg m/s
A Force of 12 N West acts on a 4.0 kg ball for 3.0 s. The ball is at rest.
A) 12 N-s B) 36 N-s C) 48 N-s
A) 12 N-s B) 36 N-s C) 48 N-s
Who experiences a greater Impulse or change in momentum?
Don’t try this with your car!
Details about the car:
m = 1000 kg
vi = 20 m/s
vf = -10 m/s
∆pcar = ?
Details about the truck:
m = 3000 kg
vi = 0 m/s
vf = 10 m/s
∆ptruck = ?
Change in momentum of the car is equal and opposite to that of truck
Remember that this is another view of the 3rd law
Conservation of Momentum
Collisions and explosions are everywhere. What takes place in these situations is governed by:
The LAW of CONSERVATION OF MOMENTUM
The momentum before a collision or explosion is equal to the momentum after.
Newton's Cradle
MOMENTUM IS A CONSERVED QUANTITY.
While the objects might each experience a change in momentum as a result of the collision the total momentum remains the same.
This is a closed system, ie no extra force from a third object came into the situation.
CONSERVATION OF MOMENTUM IS A LAW
3 basic scenarios
Elastic collisions occurs when the two objects "bounce" apart from each other when they collide
Inelastic collisions occurs when two objects collide and do not bounce away from each other.
Perfectly elastic and inelastic examples
Explosions- objects originally at rest separate.
The cannon’s movement is called recoil.
These scenarios can be mixed and matched in real life.
In reality collisions occur across the spectrum of elastic to inelastic. More collision info
Lots of variations exist within these 3 scenarios
In order to solve problems we need to write an equation which summarizes what happens in the “collision” or “explosion”. Follow this general strategy.
The only equation on the reference table is pbefore=pafter
For each of the following animations determine if it is elastic or inelastic and write a general equation in the format m1b etc.
1
2
3
4
6
5
1
pb=pa
elastic
m1v1b + m2v2b = -m1v1a + m2v2a
m1-car = 1000kg
m2 – truck = 3000kg
v1b= 20 m/s
v2b = 0
v1a= -10 m/s
v2a = 10 m/s
2
inelastic
pb=pa
m1v1b + m2v2b = (m1 + m2) va
When masses combine the only have one velocity. In this case, va
3
inelastic
pb=pa
m1v1b + m2v2b = (m1 + m2) va
V2b only relates to forward motion so the fact that it had vertical velocity does not matter
4
pb=pa
elastic
m1v1b + m2v2b = m1v1a + m2v2a
5
pb=pa
elastic
m1v1b + -m2v2b = -m1v1a + m2v2a
6
inelastic
pb=pa
m1v1b + (-m2v2b) = -(m1 + m2) va
If mass gets bigger velocity gets smaller
mbvb=(m1+m2)ava
Try these interactive momentum “applets”
Air Track "ScienceJoyWagon"
Cart JumpS
AstronautSpace
Rocket in space
air table
To combine momentums that are not on the same axes you follow vector rules
Use Pythagorean theorem and tan-1 to find momentum of each car after collision.
PRACTICE PROBLEMS
Case 1: Explosion
A cannon with clown are initially at rest. The clown with a mass of 100kg leaves the cannon with a velocity of 15m/s. What is the recoil velocity of the cannon?
Bullet is (0.04Kg) with realistic velocity (300m/s). What is the velocity of the person (60kg) once hit with the bullet.