Correct Representations of the Momentum Principle

dimanche 31 août 2014

1. The problem statement, all variables and given/known data

There are two parts to this question...



a)Which of the following are correct representations of The Momentum Principle? (assuming a small-enough Δt whenever it shows up)



1) [itex]\frac{Δ\vec{p}}{Δt}[/itex] = [itex]\vec{F}[/itex]|| + [itex]\vec{F}[/itex]

2) For every action there is an equal and opposite reaction.

3) pf, y = pi, y + Fnet, yΔt

4) [itex]\frac{d\vec{p}}{dt}[/itex] = [itex]\vec{F}[/itex]net

5) [itex]\vec{p}[/itex]f = [itex]\vec{p}[/itex]i + [itex]\vec{F}[/itex]netΔt

6) [itex]\vec{p}[/itex] = [itex]\vec{F}[/itex]netΔt

7) pf, x = pi, x + Fnet, xΔt

8) pf, z = pi, z + Fnet, zΔt

9) [itex]\vec{r}[/itex]f = [itex]\vec{r}[/itex]i + [itex]\vec{v}[/itex]avgΔt

10) [itex]\vec{F}[/itex]=m[itex]\vec{a}[/itex]

11) The momentum of a system is conserved.

12) The rate of change of momentum of a system is proportional to the net external force on the system.



b) Which of the following are true statements? (again, assuming a small-enough Δt)

1) [itex]\vec{p}[/itex] = [itex]\vec{F}[/itex]netΔt

2) [itex]\vec{p}[/itex]f = [itex]\vec{p}[/itex]i + [itex]\vec{F}[/itex]netΔt

3) The rate of change of momentum of a system is proportional to the net external force on the system.

4) For every gravitational and electrostatic force that one object exerts on another, there is an equal and opposite reaction force from the second object on the first.

5) pf, z = pi, z + Fnet, zΔt

6) pf, x = pi, x + Fnet, xΔt

7) [itex]\vec{r}[/itex]f = [itex]\vec{r}[/itex]i + [itex]\vec{v}[/itex]avgΔt

8) [itex]\frac{d\vec{p}}{dt}[/itex] = [itex]\vec{F}[/itex]net

9) For every action there is an equal and opposite reaction.

10) [itex]\frac{Δ\vec{p}}{Δt}[/itex] = [itex]\vec{F}[/itex]|| + [itex]\vec{F}[/itex]

11) [itex]\vec{F}[/itex]=m[itex]\vec{a}[/itex]

12) pf, y = pi, y + Fnet, yΔt

13) The momentum of a system is conserved.





2. Relevant equations

Relevant equations are basically listed above.





3. The attempt at a solution

My first attempt was this...

a) 3,5,6,7,8,11,12

b) 1,2,3,4,5,6,9,12,13



My second attempt is this...

a) 2,3,4,5,6,7,8,11,12

b) 1,2,3,4,5,6,7,8,9,11,12,13

both of which are wrong. I'll talk about why I don't think it is the ones I didn't choose as that will be easier.



1a - I didn't think that all of the forces or the net force can be summed up as the sum of the parallel forces and the perpendicular forces.

9a - I didn't think that equation is a correct representation of the Momentum Principle as that has to do with velocity not momentum (more precise it is the velocity update formula)

10a - I wasn't sure if the equation for Force was a representation of the Momentum principle.



10b-Again I didn't think that all of the forces or the net force can be summed up as the sum of the parallel forces and the perpendicular forces.



Any help would be appreciated in explaining why I am wrong as I only get three submissions and I've used two already haha. Thanks.





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