Could someone help me with circular motion?

Daniel S

Can someone help me with this question? I've spent a while looking through notes and I can't seem to find anything on it. It looks pretty easy but I can't seem to do it. I'm getting all sorts of answers for it from trying different things.



I've gotten everything from 23.44m/s to 780m/s (which is completely wrong) for max possible speed.

TheChizler

Have you drawn nice big diagrams, labelling every force and breaking all of them into vertical and horizontal components? Always helps me to get everything in order in my head.

Daniel S

Is this right so far?

N = 700(9.81)+4000 = 10,867 N
F = (Mu)sN = 0.8(10,867)
F = ma
Therefore a = 12.42m/s^2

a=v^2/R

v=29.48m/s or 106.15km/h

TheChizler

It seems like you have a lot of assumptions to make, such as the downward aerodynamic forces remaining constant with changing speed for part b, and guessing where the car starts to accelerate out of the corner. Be sure to state all assumptions.

Daniel S

I don't really understand part b, surely if he accelerates by 6m/s^2 more than a second before the end of the corner he's going off right? Do I just work out where is the soonest place he can start accelerating?

TheChizler

I'm not really sure what the lecturer expects from you in part b. I suppose the best you can do is state that he starts accelerating at some point, either at the start or halfway maybe (stating just how large the corner is, e.g. the length of the arc in metres or angle in degrees). If you ever get unsure about this in the exam just ask someone to find the lecturer.

For part c you're going to get nowhere unless you see sines and cosines in the equation. You could either resolve all forces wrt the page or to the race track, though one is probably more efficient than the other. I tried c and got like 76.9km/h as your max speed, but that's not right as the car wont slip on the flat track at 100km/h. Just do everything slowly and write everything out. Email the lecturer maybe about the unclear bits in the paper, and what he expects you to assume in this situation.

Daniel S

For part C is this correct?

N= 700(9.81) + 4000Cos10 = 10,806.2N

μsN= 0.8 (10,806.2) + 4000Sin10 = 9340N

9340/700=a

a=V^2/R

V=30.5m/s or 110.1km/h

Still don't understand what they're asking for in part B

Daniel S

TheChizler wrote: »

I'm not really sure what the lecturer expects from you in part b. I suppose the best you can do is state that he starts accelerating at some point, either at the start or halfway maybe (stating just how large the corner is, e.g. the length of the arc in metres or angle in degrees). If you ever get unsure about this in the exam just ask someone to find the lecturer.

For part c you're going to get nowhere unless you see sines and cosines in the equation. You could either resolve all forces wrt the page or to the race track, though one is probably more efficient than the other. I tried c and got like 76.9km/h as your max speed, but that's not right as the car wont slip on the flat track at 100km/h. Just do everything slowly and write everything out. Email the lecturer maybe about the unclear bits in the paper, and what he expects you to assume in this situation.

I was thinking of saying:

(6.15/6)x29.48=30.217 m from the end of corner is the earliest he could start accelerating. Otherwise he'll hit the max velocity and skid.

TheChizler

Right after careful consideration I have deduced that v_max = 34.04 m/s = 122.55 km/h.

For part b anything that shows that you understand the concepts and are able to user the correct methods should get you the majority of the marks. So yeah, either deduce at what point he can begin to accelerate without sliding, or pick a point where he begins and deduce whether he will slide or not. Just be sure to state your objective at the start.

For part c if you resolve the forces with respect to the slope of the track you should have 7 forces in play.

The centripetal force components at 10 degrees/horizontal to the track (outwards), and normal (down) to the track.
The weight of the car both horizontal (inwards) and normal (down) to the track.
The aerodynamic force normal (down) to the track only.
The resultant force the track exerts on the car so the car doesn't sink into the track, normal (up) to the track.
The force provided by the static friction horizontal (inwards) to the track.

Equate opposing forces, starting with vertical, convert to horizontal via the wheel friction and resolve these.

TheChizler

Here's a diagram explaining the above: