Momentum Kleppner Classical Mechanics Freight Car and Hopper

[MARX]

Homework Statement

Freight car and hopper*
An empty freight car of mass M starts from rest under an applied force F. At the same time, sand begins to run into the car at steady rate b from a hopper at rest along the track.

Find the speed when a mass of sand m has been transferred.

Homework Equations

attached

The Attempt at a Solution

attached

The solution answer has an extra b*t in the denominator and + answer. Where is the flaw in my method? Now I understand this can be done shorter using impulse and exact values but I prefer the more general approach and deduce specific cases at the end. Thanks

 

[haruspex]

Why do you have v-Δv instead of v+Δv?
There are some terms that are rather blurry in the image. Looks like erased or half erased. In particular, you seem to have a v₀b term which should be a v(t)b term, i.e. affected by the varying velocity.
The ability to upload images is really for diagrams and textbook extracts. It is a lot easier read and to refer to specific lines of working that is typed in.

 

[MARX]

Why do you have v-Δv instead of v+Δv?
There are some terms that are rather blurry in the image. Looks like erased or half erased. In particular, you seem to have a v₀b term which should be a v(t)b term, i.e. affected by the varying velocity.
The ability to upload images is really for diagrams and textbook extracts. It is a lot easier read and to refer to specific lines of working that is typed in.

Sorry it just takes lots of time to type and I work out lots of problems so trying to use time efficiently!Next time I will use ink and make it more neat apologies.
as for v-Δv due to the added mass shouldn't the velocity decrease according to Conservation of Momentum. Wrong? I tried changing the sign but that only switches final sign and does not produce right answer.
There is no V₀, it is meant to be V_(t) sorry

 

[Orodruin]

Sorry it just takes lots of time to type and I work out lots of problems so trying to use time efficiently!Next time I will use ink and make it more neat apologies.

I strongly suggest that you type it out here instead of on paper and make a photo. Remember that, while it might be more "efficient" for you, it certainly is not for the people you are asking to help you (for free). People here are much more likely to help you if they see that you have put at least some effort into making that job easier for them instead of expecting them to cater to what is convenient for you.

as for v-Δv due to the added mass shouldn't the velocity decrease according to Conservation of Momentum. Wrong?

What makes you think that $\Delta v$ cannot be negative? A good way to avoid sign errors is to always define the change in something as positive when that something increases. Like haruspex, I have real problems reading what you have written so I cannot help you more than that since that is all you typed out.

 

[haruspex]

tried changing the sign but that only switches final sign and does not produce right answer.

It should have fixed both problems. Please post your reworking (typed!)

 

[MARX]

It should have fixed both problems. Please post your reworking (typed!)

I got the right answer thank you so much for your help.
For other questions I will continue to snap images of my work I will make sure my handwriting next time is clear and I will use a pen I am sorry I will not type it typing takes lots of time especially the kind of questions I attempt are not the shortest.. if that's something you can't help me with I totally understand I'll just wait for someone who's willing to.
Thanks again and I am grateful.

 

[Orodruin]

For other questions I will continue to snap images of my work I will make sure my handwriting next time is clear and I will use a pen I am sorry I will not type it typing takes lots of time especially the kind of questions I attempt are not the shortest

Let me remind you of item 5 in https://www.physicsforums.com/threads/guidelines-for-students-and-helpers.686781/
It deals specifically withthis issue and if you continue doing this you may find it increasingly difficult to find people who are willing to help you. Even if your posts are not outright deleted, you make life more difficult for the people you are asking to help you. If you cannot be bothered to type something into make it easier for us to help you, why should we take the time to help you?

 

[MARX]

Let me remind you of item 5 in https://www.physicsforums.com/threads/guidelines-for-students-and-helpers.686781/
It deals specifically withthis issue and if you continue doing this you may find it increasingly difficult to find people who are willing to help you. Even if your posts are not outright deleted, you make life more difficult for the people you are asking to help you. If you cannot be bothered to type something into make it easier for us to help you, why should we take the time to help you?

Thank you for your help as well.

 

[vela]

Typing takes lots of time especially the kind of questions I attempt are not the shortest.

I encourage you to invest a little time to learn the basics of LaTeX. It's not hard. Despite your misgivings, typing your work out doesn't actually take that long. We're not asking you to type out every single step of your work, but enough detail so we can spot where the problem lies.

 

[jbriggs444]

I encourage you to invest a little time to learn the basics of LaTeX. It's not hard. Despite your misgivings, typing your work out doesn't actually take that long. We're not asking you to type out every single step of your work, but enough detail so we can spot where the problem lies.

The effort of transcribing the work and prettying it up can often reveal problems without even having to post the result.

 

[rude man]

You don't need to learn LaTex to post in typing. Click on the Σ symbol at the far right of the toolbar and it will take care of most situations. I myself lived for years and years without LaTex until I finally had to use it to write a paper. I agree it's not that hard to assimilate - maybe 1 day's work. But it does take extra time to type which may be a factor if you're that busy.