You are Here: Home >< Maths

# Help with Mechanics - Circular Motion watch

1. So the question states;
"A corner on a flat surface forms a circular arc with the radius 50m. A car travels around the corner at 14m/s without sliding. What information does this give for the value of the coefficient of friction between the tyre and the road surface?"
So far I've discovered the angular velocity which is 0.28rad/s (if I calculated that correctly). But I'm not sure where to go from there?
2. (Original post by abbiechantellex)
So the question states;
"A corner on a flat surface forms a circular arc with the radius 50m. A car travels around the corner at 14m/s without sliding. What information does this give for the value of the coefficient of friction between the tyre and the road surface?"
So far I've discovered the angular velocity which is 0.28rad/s (if I calculated that correctly). But I'm not sure where to go from there?
Think about the centripetal forces involved here. Which centripetal force enables the car to travel through the arc without sliding off it?

Equate this centripetal force with an expression which you should be familiar with:

Think about the centripetal forces involved here. Which centripetal force enables the car to travel through the arc without sliding off it?

Equate this centripetal force with an expression which you should be familiar with:

This is the right idea, but we're looking for an inequality, not an equation. Bear in mind that the coeff. of friction is used in the expression for *limiting* friction.
4. (Original post by atsruser)
This is the right idea, but we're looking for an inequality, not an equation. Bear in mind that the coeff. of friction is used in the expression for *limiting* friction.
Technically what he says is exactly right, you just introduce the inequality at a later stage.

CF = mrw^2
CF = friction
Friction <= u R (where u is coefficient of friction and R is reaction)
Therefore (CF/R) <= u
u >= (mrw^2)/R
5. Thank you all for your help! Any chance I could ask about a few more? I'm finding these questions fairly tricky
6. (Original post by abbiechantellex)
Thank you all for your help! Any chance I could ask about a few more? I'm finding these questions fairly tricky
7. (Original post by Darth_Narwhale)
"A flat road is built so that any vehicle turning onto it can travel up to 21m/s without sliding happening. In the worst weather, an engineer speculates that the coefficient of friction is as low as 1/8. Calculate the lowest radius the corner can have."
8. At lowest value of u:
CF = mrw^2
CF = friction
max Friction = u R (where u is coefficient of friction and R is reaction = mg)
Friction = umg
CF = umg
mrw^2 = umg
rw^2 = ug
r = ug/(w^2)
9. Ah thank you so so much!
Sorry to be a pain but I have a few more hahah
"One end of a light inextensible string 1m is attached to stationary point A and particle P with mass m is attached on the other side. A second string 1m long is attached to P and stationary point B so that B is lying 1.5m vertically under A. The particle is made to move in a horizontal circle with the uniform angular velocity w. Calculate the lowest value for w so that the strings are tight."
10. (Original post by abbiechantellex)
Ah thank you so so much!
Sorry to be a pain but I have a few more hahah
"One end of a light inextensible string 1m is attached to stationary point A and particle P with mass m is attached on the other side. A second string 1m long is attached to P and stationary point B so that B is lying 1.5m vertically under A. The particle is made to move in a horizontal circle with the uniform angular velocity w. Calculate the lowest value for w so that the strings are tight."
This is my working. The top left are two equations for tension, which allows us to cancel out one of the two tensions. The top right is the equation for cancellation of the tension. I then say that, as T2 is smaller than T1, the strings are only taught when T2 >= 0, which gives the inequality on the right.

The bottom half is just me substituting everything in.

It's a bit messy, so just shout if you need me to explain anything
11. (Original post by Darth_Narwhale)
Technically what he says is exactly right, you just introduce the inequality at a later stage.
This is true - he wasn't incorrect, but I felt that what he wrote could come across as misleading - the inequality is the crux of the question.

CF = mrw^2
CF = friction
Friction <= u R (where u is coefficient of friction and R is reaction)
Therefore (CF/R) <= u
u >= (mrw^2)/R
Please don't give complete solutions - they are forbidden by the forum power's-that-be.
12. (Original post by atsruser)
This is true - he wasn't incorrect, but I felt that what he wrote could come across as misleading - the inequality is the crux of the question.

Please don't give complete solutions - they are forbidden by the forum power's-that-be.
My mistake, I wasn't aware of that

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: January 16, 2017
Today on TSR

### TSR Pub Quiz 2018 - Anime

Start time will be 6 PM tonight

### University open days

Wed, 21 Nov '18
• Buckinghamshire New University
Wed, 21 Nov '18
• Heriot-Watt University
Wed, 21 Nov '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