Roller coaster Conservation of Energy problem

In summary, at the bottom of the loop, the person has normal force and the force of gravity. The difference in these two forces is 6 mg's. This is why on a roller coaster with a circular vertical loop, the person's weight is six times their weight at the bottom of the loop.
  • #1
joseg707
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Homework Statement


Show that on a roller coaster with a circular vertical loop, the difference in your apparent weight at the top of the circular loop and the bottom of the loop is 6 g's--that is six times your weight. Ignore friction. Show also that as long as your speed is above the minimum needed, this answer doesn't depend on the size of the loop or how fast you go through it.


Homework Equations


PE(1)+KE(1)=PE(2)+KE(2)
F=ma

The Attempt at a Solution


I'm not really sure what it is that they are asking me to solve for. I set up my problem from the the bottom of the loop. The bottom of the loop is 1 and the top of the loop is 2.

KE(1)=PE(2)+KE(2)

.5mv2=2mgr+.5mv2.

The mass cancels out but I don't know how to prove that at the top of the loop a persons weight at the top of the loop is 6x greater.

Things I tried

.5mv^2=12mgr+3mv^2

2.5mv^2=12mgr

2.5v^2=12gr

I gave up on that because I really didn't see how it was useful for what I needed to find. Can someone help me please?
 
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  • #2
One must realize that the speed at the bottom v1 is greater than the speed at the top v2.

One must find v2, for which one uses the constraint the v2 is the minimum needed to maintain contact with the track, i.e. not fall. So what is v2?

Then apply the conservation of energy .5mv12=2mgr+.5mv22.

Think of centripetal force.
 
  • #3
Ok so v22=gr.
I substitute that into my energy equation and I get:
.5mv12=2mgr+.5mgr
After all the algebra I get
v=[tex]\sqrt{5gr}[/tex]
I don't see how this is a step in proving that a person's weight is 6 times their normal weight at the top of the loop. Could you explain what is happening please?
 
  • #4
At the bottom of the loop, what are the forces on the person?
 
  • #5
Normal force and the force of gravity.
N-mg=ma
N-mg=mv2/r
N-mg=m5gr/r
N=5mg+mg
N=6mg

I see now! Thank you very much! =)
 

FAQ: Roller coaster Conservation of Energy problem

What is the concept of conservation of energy in the context of roller coasters?

The conservation of energy states that energy cannot be created or destroyed, but it can be transformed from one form to another. In the context of roller coasters, this means that the total amount of energy at any point in the ride remains constant, even though it may change forms.

How does potential energy play a role in roller coaster conservation of energy?

Potential energy is the energy an object has due to its position or height. In a roller coaster, potential energy is gained as the coaster climbs to the top of a hill and is converted to kinetic energy as it travels down the hill. The conservation of energy ensures that the total amount of potential and kinetic energy remains constant.

Why is friction important to consider in the conservation of energy for roller coasters?

Friction is a force that opposes motion and converts kinetic energy into other forms, such as heat or sound. In the context of roller coaster conservation of energy, friction plays a role in slowing down the coaster and converting its kinetic energy into other forms. This means that the total energy of the coaster decreases over time.

What happens when a roller coaster does not have enough kinetic energy to complete a loop or hill?

If a roller coaster does not have enough kinetic energy to complete a loop or hill, it will come to a stop or even roll backwards. This is because the conservation of energy states that the total energy must be enough to overcome the force of gravity and continue the motion of the coaster.

Can the conservation of energy be violated in a roller coaster ride?

No, the conservation of energy is a fundamental law of physics and cannot be violated. However, due to external factors such as friction and air resistance, some energy may be lost or converted to other forms, but the total energy remains constant throughout the ride.

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