Calculating Centripetal Acceleration and Normal Force on a Roller Coaster Loop

In summary, the roller coaster ride contains a circular loop with a car of mass m starting at rest at point A and traveling around the loop in a counter clockwise direction from B to C to D to E and back to B. The centripetal acceleration at points B and C can be found using the equations Fnet = mv^2/r and ac = v^2/r. The normal force at point B is equal to the gravitational force (Fg) due to the car's weight. At point C, the centripetal acceleration is determined by the car's speed after losing one radius worth of potential energy.
  • #1
Shatzkinator
53
0

Homework Statement


The diagram below shows a roller coaster ride which contains a circular loop of radius r. A car of mass m begins at rest from point A and moves down the frictionless track from A to B where it then enters the vertical loop (also frictionless), traveling once around the circle from B to C to D to E and back to B, after which it travels along the flat portion of the track from B to F (which is not frictionless).

1. Find the centripetal acceleration of the car at points B and C.
2. Find the normal force at point B.

Homework Equations


Fnet = mv^2/r
ac = v^2/r


The Attempt at a Solution


1. I got Ac = Fn/m - g for point B. For point C i got Ac = -Fn/m + g
2. I got Fn = mv^2/r + g


I got -2 marks off for this problem.. where did I go wrong?

By the way, the loop goes counter clockwise (B, C, D, E)
 
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  • #2
If those are your answers, I'd say you didn't answer the question.

They asked for centripetal acceleration. Just curious why you involved g?
 
  • #3
LowlyPion said:
If those are your answers, I'd say you didn't answer the question.

They asked for centripetal acceleration. Just curious why you involved g?

Fn - mg = mAc
 
  • #4
Shatzkinator said:
Fn - mg = mAc

And what is Fn?
 
  • #5
LowlyPion said:
And what is Fn?

Fn is.. normal force? What do you mean. There is no value given.
 
  • #6
Well you are expected to come up with a value for that. Your answer is no answer at all.

For instance what is it at the point B?

I can't see your diagram but I presume it is at the base of the loop where the horizontal angle is 0°. So what is the Fn at that point?
 
  • #7
LowlyPion said:
Well you are expected to come up with a value for that. Your answer is no answer at all.

For instance what is it at the point B?

I can't see your diagram but I presume it is at the base of the loop where the horizontal angle is 0°. So what is the Fn at that point?

Fn at point B is Fg ??
 
  • #8
Shatzkinator said:
Fn at point B is Fg ??

Which means what as far as the centripetal acceleration?
 
  • #9
LowlyPion said:
Which means what as far as the centripetal acceleration?

it equals 0? =S
 
  • #10
Shatzkinator said:
it equals 0? =S

That might have made a better answer then. Now if your point B is just a hair past the 0° point its acceleration will be v2/r. In fact it may be open to debate whether right at B there is centripetal acceleration depending on how you want to interpret the drawing, (which I am disadvantaged in not being able to see).

What I can tell you is that answering Fn - mg as the centripetal acceleration is not showing how much you should know.
 
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  • #11
LowlyPion said:
That might have made a better answer then. Now if your point B is just a hair past the 0° point its acceleration will be v2/r. In fact it may be open to debate whether right at B there is centripetal acceleration depending on how you want to interpret the drawing, (which I am disadvantaged in not being able to see).

What I can tall you is that answering Fn - mg as the centripetal acceleration is not showing how much you should know.

Right understandable.

So at point C, what would be the appropriate answer if the tangent to the circle at this point is perpendicular to the x axis?
 
  • #12
I will guess though that it is at 3 o'clock.

In which case the centripetal acceleration will be determined by its speed after losing 1 radius worth of potential energy.
 
  • #13
LowlyPion said:
I will guess though that it is at 3 o'clock.

In which case the centripetal acceleration will be determined by its speed after losing 1 radius worth of potential energy.

I don't understand. We didn't learn potential energy yet.. How can I calculate the acceleration without it?

And also for part B, There is no way to get value for Fn because there is no mass??
 
  • #14
That's surprising, because these problems are typically addressed in terms of kinetic and potential energy.

Specifically

1/2*mVC2 = 1/2mVB2 - m*g*(HC-HB)

The m cancels out and you are left with

Vc2 = VB2 - 2*g*(HC-HB)

ac = 1/R*(VB2 - 2*g*(HC-HB))

And what is Hc - HB ?

That's simply R, so

ac = 1/R*(VB2 - 2*g*R)
 

1. What is the Roller Coaster Loop Problem?

The Roller Coaster Loop Problem is a classic physics problem that involves calculating the minimum required height for a roller coaster loop in order for a passenger to safely complete the loop without falling out. It is used to understand the relationship between centripetal force and gravitational force.

2. How is the minimum required height calculated?

The minimum required height is calculated using the energy conservation principle, which states that the total energy at the top of the loop must be equal to the total energy at the bottom of the loop. This means that the sum of the kinetic energy and potential energy at the top of the loop must be equal to the kinetic energy and potential energy at the bottom of the loop.

3. What factors affect the minimum required height?

The minimum required height is affected by the speed of the roller coaster, the radius of the loop, and the mass of the passenger. As the speed or radius of the loop increases, the minimum height also increases. Similarly, as the mass of the passenger increases, the minimum height also increases.

4. Why is the minimum required height important for roller coaster design?

The minimum required height is important for ensuring the safety of passengers on roller coasters. If the height of a loop is too low, the passenger may not have enough speed to complete the loop and could fall out. It is also important for designing thrilling and exciting roller coasters that can safely perform loops.

5. Can the minimum required height be calculated for any type of roller coaster?

Yes, the minimum required height can be calculated for any type of roller coaster as long as the speed, radius, and mass of the passenger are known. However, different types of roller coasters may have different minimum height requirements depending on the design and layout of the track.

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