Momentum and collisions

Question 0

Motion map

Answer 0

A series of arrow-drawings that display the magnitude of the velocity vector at given time intervals to illustrate overall acceleration

Question 1

Momentum of a single particle

Answer 1

Product of mass and constant velocity

p=m*v

Question 2

Momentum in a multi-particle system

Answer 2

Sum of each particular momentum

Σp=m1v1+m2v2+…ect

Question 3

Total momentum

Answer 3

Sum of all the objects’ momenta within a system

Σp=p1+p2

Question 4

Change in momentum

Answer 4

Δp=FΔt=∫F(t)dt

Area under the force curve in the given time period

Question 5

Impulse

Answer 5

Net change in momentum
I=Δp=FΔt=∫F(t)dt
Area under the force curve in the given time period

Question 6

Law of conservation of momentum

Answer 6

In a closed system, the amount of momentum within the system remains constant

Question 7

Units of momentum

Answer 7

Newton-seconds (Ns)

Question 8

Calculating shifts in velocity based on impact

Answer 8

m1vi1+m2vi2=m1vf1+m2vf2

Use algebra from here

Question 9

Equal mass collisions with a stationary object

Answer 9

All the momentum will be transfered,

The stationary object will carry with it the velocity vector, both magnitude and direction

Question 10

Elastic collisions

Answer 10

The two objects bounce off one another and momentum is transfered

Question 11

Inelastic collisions

Answer 11

Two objects stick together and their total mass reduces the final velocity

Question 12

Measuring elasticity of a collision (with constant acceleration and a stationary object)

Answer 12

Coefficient of restitution
Cr=√(bounce height/drop height)
Or for horizontal systems
Cr=√(final distance from impact/starting dfi)

Question 13

Describing vectors in momentum

Answer 13

p=(pi,pj,pk)

Question 14

Converting velocity vectors to momentum vectors

Answer 14

Multiply each i j k component by object mass

Question 15

Converting acceleration vectors into momentum function vectors

Answer 15

Calculate the indefinate integral ∫a(t)+Vo=v(t) for each of the i j k directions then multiply by mass to find each component-function p(t)=m*v(t)

Question 16

Converting force vectors into momentum function vectors

Answer 16

Divide each force i j k component by object mass to find acceleration components. Calculate the indefinate integral ∫a(t)+Vo=v(t) for each of the i j k directions then multiply by mass to find each component-function p(t)=m*v(t)

Question 17

Converting position function vectors into momentum function vectors

Answer 17

Take the derivative ∂s(t)=v for each i j k component, multiply by object mass to find p=m*v in each component direction

Question 18

Momentum (given an invarient mass)

Answer 18

p=γMo(v)

Where γ is 1/√(1-(v/c)^2)

Question 19

Momentum in an i j k vector-component direction given velocity vector, kinetic energy function (T), and potential energy function(V)

Answer 19

pj=∂(T(t)-V(t))/∂vj

Question 20

Adjusting momentum in a vector field with a given vector potential

Answer 20

It becomes ‘canonical momentum’
P=m(v)+e*A

‘A’ being the vector field potential

Question 21

Momentum given kinetic energy (T) and mass (m)

Answer 21

p=√(2T*m)

Question 22

Drawing motion maps

Answer 22

X and y axis are x and y coordinates

1) Draw a dot for the objects position each second
2) Draw arrows in the vector-direction of motion
3) the length of the arrows reflect the velocity