Correct Representations of the Momentum Principle

[The Wanderer]

Homework Statement

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) $\frac{Δ\vec{p}}{Δt}$ = $\vec{F}$_|| + $\vec{F}$_⊥
2) For every action there is an equal and opposite reaction.
3) p_{f, y} = p_{i, y} + F_{net, y}Δt
4) $\frac{d\vec{p}}{dt}$ = $\vec{F}$_net
5) $\vec{p}$_f = $\vec{p}$_i + $\vec{F}$_netΔt
6) $\vec{p}$ = $\vec{F}$_netΔt
7) p_{f, x} = p_{i, x} + F_{net, x}Δt
8) p_{f, z} = p_{i, z} + F_{net, z}Δt
9) $\vec{r}$_f = $\vec{r}$_i + $\vec{v}$_avgΔt
10) $\vec{F}$=m$\vec{a}$
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) $\vec{p}$ = $\vec{F}$_netΔt
2) $\vec{p}$_f = $\vec{p}$_i + $\vec{F}$_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) p_{f, z} = p_{i, z} + F_{net, z}Δt
6) p_{f, x} = p_{i, x} + F_{net, x}Δt
7) $\vec{r}$_f = $\vec{r}$_i + $\vec{v}$_avgΔt
8) $\frac{d\vec{p}}{dt}$ = $\vec{F}$_net
9) For every action there is an equal and opposite reaction.
10) $\frac{Δ\vec{p}}{Δt}$ = $\vec{F}$_|| + $\vec{F}$_⊥
11) $\vec{F}$=m$\vec{a}$
12) p_{f, y} = p_{i, y} + F_{net, y}Δt
13) The momentum of a system is conserved.

Homework Equations

Relevant equations are basically listed above.

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.

 

[Fredrik]

Those lists are much too long for us to comment on them one by one. You will have to list the ones you want to discuss, and for each one, attempt to explain why it should or shouldn't be included in your answer.

I started answering b10 because I thought the ones you listed at the end were the ones you wanted help with. This is a partial answer for b10: (We can't give you complete answers in the homework forum).

dp/dt is the force. Do you understand why? So the statement is just saying that the force can be split up into two component vectors that are orthogonal to each other. Can you come up with a reason why this should or shouldn't be possible?

Edit: OK, so you probably saw the much too complete answer I gave you for b10 before I realized my mistake and replaced it with the hints above.

 

[The Wanderer]

Okay so I was wrong on b10 and a1 haha. I was looking at it wrong I was thinking it was saying all forces are either parallel or perpendicular to the momentum but what it is saying is all the component vectors can be split into those two pairs which makes sense to me. Really you don't have too look at them all but mostly a9 and a10 as I am quite confident the ones I did choose as correct are correct but I wasn't sure on a1, a9, a10, and b10, but you answered b10 and a1.

 

[Fredrik]

OK, so the ones you listed at the end are the ones you want help with. That's good to know. Unfortunately I don't have time right now, so I'm leaving it for someone else.

 

[The Wanderer]

Yeah maybe I should have made that more clear. Thank you very much for your help.

 

[doans]

How did you answer this question? I have the same one and I'm struggling on it.

 

[berkeman]

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