[tnhoots]

A roller coaster has a mass of 510kg when fully loaded with passengers. The radius at point A is 10.0 m and the radius at point B is 15.0 m.

-If the vehicle has a speed of 19.6 m/s at point A, what is the force exerted by the track on the car at this point? (N)

-What is the maximum speed the vehicle can have at B and still remain on the track? (m/s)


*For the first problem I thought you would use the equation EF=m (v^2 / r). Which would be EF=510 (19.6^2 / 10.0). Which equals 510*(384.16/10.0). Equals 19592.16. However, this is wrong! Isn't that the right equation?

*For the second problem, I'm not sure where to start. But I'm assuming that I will need the correct force value before I can begin.

Any suggestion as to where I'm going wrong?

[Capuchin]

Assuming that A is the bottom of a circular dip, and B is at the top of a circular hump:

In the first question you forgot to factor in the car's weight.

you need to work out centripetal acceleration

(in the upwards direction)

then the full acceleration,



remember these are in different directions, so you need to select a direction as positive.

then you can use our favorite equation:



This should give you the force you are after.

For question 2 you can use the equation you stated:



This is the centripetal force needed to go speed v around a circle radius r. You know F though as the only force acting on the car is gravity. You know r and m also as constants. V will give you the maximum speed because F is the maximum force gravity can provide, if you go slower than the maximum speed v, the force is cancelled out by the track pushing up on the car.

Hope this helps and my assumptions are correct.

How did you get on with the hawk question by the way? I see you didn't reply to my answer there. - You also haven't rated any of my answers, am i being helpful? I'd like to know.

I've answered a number of questions from you and I assume they've been helpful because you don't reply anymore. Could you give some feedback please when you solve a question because of my help? I like to know when I'm making sense.

Thanks, Capuchin.

[dmatos]

I'd rate you, Capuchin, but apparently, I need to spread some reputation around first. I would make one note on your explanation, though. "Weight" is a dangerous word to use. Yes, technically, and scientifically, it is a measure of the force of gravity acting on an object. Unfortunately, colloquially it has earned the connotative meaning of "mass."

"How much do you weigh?"
"80 kilos."

It bugs me too. I answer that it depends on the distance between my belly button and the centre of mass of the Earth.

[Capuchin]

Although I always use "mass" in every day situations, I do assume when people are talking physics they are in "physics mode" and think of weight and mass appropriately, you're probably right that they don't always do that though.

I'm not too bothered about the greenie and am much more thankful for the feedback :)

It probably comes from the fact that scales weigh you, therefor people assume they read out your "weight" whereas they actually convert it into your mass before reading out.

[tnhoots]

Capuchin, you have been doing an awesome job helping me out these past few weeks. I just get so caught up in trying to solve the problems and complete work that it kind of takes over my train of thought. Plus, I haven't navigated completely around this site yet, so I'm kind of clueless to the whole rating system. Sorry to make you feel unappreciated. However, that is not the case. I'm grateful for any help/suggestions you offer! THANKS!

For the equation
a=ag+acp
the ag would just be 9.8 correct? Because 9.8 m/s^2 is the value of gravity. Then add that to the centripetal acceleration to find a?

[Capuchin]

Yes, but don't forget that the vectors are in opposite directions, so one of them has a "negative magnitude" (positive magnitude in a negative direction).

Acp is pushing up on the car, ag is pulling down on it.

(to rate you can click the "rate this answer!" button under a post, but replying like you did here is plenty enough for me :))

[tnhoots]

So here is my thinking for the first problem...
cent. Acceleration equals v^2/r = 19.6^2/10.0 = 38.416
full acceleration equals -9.8+38.416 = 28.616

F=ma
F=510kg (28.616)
F=14594.16 N

Question 2 would be
510kg(19.6^2 / 10/0)
However, using that equation gives us the Force, not speed.

[Capuchin]

Your answer for question 1 looks like what I was saying, yes.

why did you put v in for question 2? You don't know the speed at that point! Read my answer for question 2 again. You need to put F, m and r in to get a value for v.

[tnhoots]

My answer of 14594.16N which I got for the first problem is incorrect. I put the numbers into the formula just as you said and as I thought they would go; however, it is incorrect. Work:
cent. Acceleration equals v^2/r = 19.6^2/10.0 = 38.416
full acceleration equals -9.8+38.416 = 28.616
F=ma
F=510kg (28.616)
F=14594.16 N


I am not sure where the mistake is. Also for problem 2- I got confused and wanted to use the velocity that it gave us for point A. That was my mistake. For this problem will I use the force that I found for part A, when I find the correct force?

[Capuchin]

Why is it incorrect? - sorry I see an error, you need to add the gravitational acceleration to the centripetal acceleration because the track is pushing against gravity, and is providing centripetal force, so it's 9.8+38.416

Is my assumption that A is the bottom of a dip and B is the top of a hump correct? You never clarified

No you don't need anything for part B, it's the force due to gravity.

[tnhoots]

Yes, you are correct. Point A is a dip in the track and point B is at the top of a hill on the coaster. So, for part B I use the equation F=m(v^2/v). Mass would be 510kg, radius would be 15.0m, force would be 9.8 m/s^2 because of gravity. And I will solve for v correct?

[tnhoots]

I am so lost on how to find the speed in part b of this question..?

[Capuchin]

F = ma where a is 9.8 and m is 510, put thie F into the equation along with r and m, rearrange for v

[tnhoots]

Ok, so I said F=ma
F=510(9.8)
F=4998
I then put that in to the equation F=m(v^2/r)
4998=510(v^2/15)
4998=7650v^2
v=.808


However, this is incorrect! Where is my mistake?

[Capuchin]

how does ??

it's

This is elementary arithmetic :p

give you a v of 12.something, which sounds about right :)