Calling all LC applied maths students..

TomSweeney

Hi there,

I do maths as a hobby and have an old Applied maths book lying about that I enjoy doing the problems.

I do not know where I have gone wrong here with this question :

Here is my workings :

Ignore the part above surrounded in red, that was just assuming witout friction, and this using a different total mass to see if I could get the expected answer.

Note from a worked example in the book this is the exact same method and still don't get the answer, the only difference is in the worked example there is no friction (smooth table)

It's driving me mad, maybe I am correct and it is 19g/28 but don't think so … as there was another similar question that I also couldn't get the correct answer - again friction was involved.

Michael Collins

What an excellent hobby.

It seems that you have left out the component of the force R that contributes to the overall force pushing down on the table. You've correctly included the 3/5R in your Eq (iii) but there should be a 4/5R downward force (from the particle) adding to the mg downward force from the wedge.

Brussels Sprout

Wow this brought back memories. I did Applied Maths myself over 20 years ago now. Just saw the thread title on the main page. I never really likes these questions. Much preferred the uniform accelerated motions ones and the firing cannon ball types questions.

On that note. I was watching the Javelin final last night and I noticed that they have a nice feature which showed the angle of the throws on the replays. Typically they seemed to throwing at an angle of 33 degrees.

I vaguely recalled a proof that we did as part of our applied maths that showed that the optimal angle for maximum distance was actually 45 degrees. I was therefore wondering why they weren't throwing it at that angle? I'm guessing that it must be something to do with the air resistance, which I think is something that wasn't considered in those proofs. Anyone know?

TomSweeney

Yes sorry, I did get the solution out - after someone else suggested I take the weight and hence the normal force from the particle into account for Friction.

TomSweeney

https://www.boards.ie/discussion/comment/122483853#Comment_122483853

Yes, it was a great course, Projectiles and relative velocity were my favourite topics, such fun - especially projectiles on the inclined plane.

Regarding 45 degrees being the optimal angle - it's true there is a nice proof of it, i might post it if I can dig it up later.

as for the 33 degrees in reality, yeah probably to do with the shape and/or air resistance.