Are You Confused About Work-Energy vs. Impulse-Momentum?

[aeb2335]

Recently I have been having issues knowing when to use the work energy principal vs. impulse momentum or using F=ma and integration.

I seem to default with all problems to integrating work done over a path but then messing it up or that not being the proper approach.

The issue seems to be that in my head they are all inter-related via integration or differentiation but I always seem to be picking the wrong one.

Is there a general approach or key words of things to look for when starting off a problem? Or perhaps what would be the most general approach that will always yield a correct result.

Has anyone else had these issues of confusion?

 

[diazona]

Well, in general you should be using an equation that incorporates at least one of the quantities you are given. So if you're given an acceleration, it's likely that you'll need F=ma, not conservation of energy.

 

[Simon Bridge]

You don't seem to have mentioned this in other threads.
Perhaps some examples of the kind of thing you get confused over will help?

note: if you are given acceleration, then you may still want to use conservation of energy methods. (W=mad - but you already knew that!)

Sounds like situations where you are provided with forces and it is not clear if you get the results through conservation of energy or by summing the forces and applying Newton's laws?

There is no sure-fire way to tell which one to use ... you could try going back over examples, and try writing out the math for each in terms of conservation of energy and in terms of summing forces, then looking to see which looks like the easiest to do.

Anything that is worded "before and after" uses conservation laws, similarly if you find there's lots of information apparently missing.

A mass sliding down a frictionless slope, from height h - and you want to know the final speed: that's conservation of energy. Similarly is an object comes to rest in distance d and you want the initial speed.

 

[aeb2335]

Both of these replies make a lot of sense the real issue I guess is when I try and solve problems for "fun" . Text book problems are usually not as much of an issue because they typically are "ready made".

Here is what I was pondering its a silly question but here it goes

A 2 cars with equivalent mass M and gas tank of volume V and with equivalent ranges and efficiencies (mpg) set off for a destination D away. Car 1 fills their gas tank only 50% calming that because the gas stations are all on the road they are traveling that the extra gas is extra weight that is not needed resulting in less work being done ergo less energy (total gas) used.

Car 2 says that he is lazy and doesn't think it will make a sizable impact and car 1 will improve their mpg only slightly.

Now my initial approach was to go the route of Work of car1= ∫ (mass of car°a - mass flow rate°a) dx

but then i remembered that this is very similar to the Tsiolkovsky rocket equation
ΔV= Ve ln (minital/ mfinal)

But this solution looks completely different and it seems the rocket equation uses an energy approach.

So what would be the better way of solving this really silly problem and how can I avoid these issues when problems are not ready made

 

[Simon Bridge]

You do want to use an energy approach since you have efficiencies to take into account. You want to express energy-use in gallons of gas.

Note - the work done to keep moving at constant speed is accounted for by the efficiency. Where weight will play a role is in accelerations... which will depend on the exact nature of the trip.

It may be that the car with less fuel carried will have to stop more often to refuel, thus having more intervals in which they do extra work.

Basically you don't have enough constraints on your system in order to reveal the behavior you are after.