You are Here: Home >< Maths

Vertical loop watch

1. A motorcyclist rides up a vertical loop of radius 40m. His engine cuts out when he has travelled an eighth of the way round the full loop.

If there is no resistance to motion, what is the minimum speed he must be travelling at this point to complete the full circle?

I drew a diagram where he starts at u m/s and forces mg and Reaction downwards, with acceleration towards the centre. Do I need to consider energy and does the fact that he is an 1/8 round the loop make a difference?
2. Firstly, the reaction shouldn't be downwards, it should be towards the centre, and the acceleration isn't necessarily towards the centre (and mostly, it isn't).

If the motorbike is to complete a full circle, what must be true of the reaction force all the way round?

You will need to consider energy, and the fact that he's an eighth of the way round tells you how much GPE he has already/how much KE he'll need to have to get to the top.
3. (Original post by Hopple)
Firstly, the reaction shouldn't be downwards, it should be towards the centre, and the acceleration isn't necessarily towards the centre (and mostly, it isn't).

If the motorbike is to complete a full circle, what must be true of the reaction force all the way round?

You will need to consider energy, and the fact that he's an eighth of the way round tells you how much GPE he has already/how much KE he'll need to have to get to the top.
The reaction force all the way round must be equal to mg cos (45) -mv^2/r ?
4. (Original post by bbrain)
Really?
5. (Original post by bbrain)
The reaction force all the way round must be equal to mg cos (45) + mv^2/r ?
That's the reaction force one eighth of the way round, make a small change in that to see what it must be at some angle theta of the way round. But what I was getting at was that it must be greater than (or equal to) 0 all the way round, particularly at the top.

Edit: should be plus, not minus. Changed the bit I quoted from you.
6. (Original post by BabyMaths)
Really?
Maths stuntmen are the most impressive.
7. Can I have some real help with the question please?

....................../´¯/)
....................,/¯../
.................../..../
............./´¯/'...'/´¯¯`·¸
........../'/.../..../......./¨¯\
........('(...´...´.... ¯~/'...')
.........\.................'.... ./
..........''...\.......... _.·´
............\..............(
..............\.............\...
8. (Original post by bbrain)
Can I have some real help with the question please?

....................../´¯/)
....................,/¯../
.................../..../
............./´¯/'...'/´¯¯`·¸
........../'/.../..../......./¨¯\
........('(...´...´.... ¯~/'...')
.........\.................'.... ./
..........''...\.......... _.·´
............\..............(
..............\.............\...
Post 5.

Related university courses

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: March 10, 2013
The home of Results and Clearing

2,195

people online now

1,567,000

students helped last year
Today on TSR

University open days

1. Sheffield Hallam University
Tue, 21 Aug '18
2. Bournemouth University
Wed, 22 Aug '18
3. University of Buckingham
Thu, 23 Aug '18
Poll
Useful resources

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

How to use LaTex

Writing equations the easy way

Study habits of A* students

Top tips from students who have already aced their exams

Chat with other maths applicants