What is the Kinetic Energy at Point A?

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You should be able to get v_0 from the first set of equations, and then substitute that into the KE equation to get the Kinetic Energy at point A.In summary, the problem involves finding the kinetic energy at point A on a rollercoaster track, which requires using the conservation of energy equation and the centripetal force equation. The first step is to establish the conservation of energy equation and solve for v_A using the centripetal force equation. Then, using the conservation of energy equation again, the initial kinetic energy can be solved for and substituted into the kinetic energy equation to find the kinetic energy at point A.
  • #1
muna580
I need help with this problem. I don't really understand what they are saying and what they are aksing me. Please can someone help me. I am guessing the whole reason I am not understandthing this problem is because of that whole "circular" concept being added to this work/energy problem.

http://img225.imageshack.us/img225/9647/untitled1jx4.jpg
 
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  • #2
muna580 said:
I need help with this problem. I don't really understand what they are saying and what they are aksing me. Please can someone help me. I am guessing the whole reason I am not understandthing this problem is because of that whole "circular" concept being added to this work/energy problem.

http://img225.imageshack.us/img225/9647/untitled1jx4.jpg
When[/URL] there is no friction or other forces that may do work, except gravity, total mechanical energy (potential and kineti) is conserved. Write the conservation of energy equation at the beginning and at the top of the curve. You will still need to find V_top-of-curve. Apply the centripetal force equation to do so, noting that as per the problem statement, only gravity acts at this point(i.e., there is no normal force that might hold the coaster to the tracks).

Then in part 2, apply the energy conservation principle again to solve for h'.
 
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  • #3
Lets lable C to be the starting point of the rollercoster.

I hope I am doing this right

Ec = mgh + (1/2)mv^2
Ea = (2/3)mgh + Ka

What is Ka? I am having a hard time sovling for Ka. I have no idea what Ka is

Ec-Ea = total mechanical engery of the concervitive force.

Please help
 
  • #4
muna580 said:
Lets lable C to be the starting point of the rollercoster.

I hope I am doing this right

Ec = mgh + (1/2)mv^2
Ea = (2/3)mgh + Ka

What is Ka? I am having a hard time sovling for Ka. I have no idea what Ka is

Ec-Ea = total mechanical engery of the concervitive force.

Please help
Kinetic Energy at a is (1/2)(m)(v_a^2). But you don't know what v_a is yet. That's when you look at the centripetal force equation at a...F = mv_a^2/r, where F = mg (the force of gravity alone). Solve for v_a, then v_0 from the first set of equations. BTW, it's Ec = Ea )Initial mechanical energy = final mechanical energy when only conservative forces act.
 
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  • #5
PhanthomJay said:
Kinetic Energy at a is (1/2)(m)(v_a^2). But you don't know what v_a is yet. That's when you look at the centripetal force equation at a...F = mv_a^2/r, where F = mg (the force of gravity alone). Solve for v_a, then v_0 from the first set of equations. BTW, it's Ec = Ea )Initial mechanical energy = final mechanical energy when only conservative forces act.

I am still confused. Look, I made this picture, to show what I understand so far. I am a little confused when it comes to circles, that is why I am not understanding the kenetic engery at point A. Can you please expalin to me step by step, how to get kenetic engery at point A.

http://img86.imageshack.us/img86/9632/untitled1ut2.jpg
 
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  • #6
muna580 said:
I am still confused. Look, I made this picture, to show what I understand so far. I am a little confused when it comes to circles, that is why I am not understanding the kenetic engery at point A. Can you please expalin to me step by step, how to get kenetic engery at point A.

http://img86.imageshack.us/img86/9632/untitled1ut2.jpg
Before[/URL] you can get the Kinetic Energy at point A, which is
[tex] KE = 1/2mv_A^2[/tex]
you first need to find [tex] v_A[/tex].

At the top of the circle , draw a free body diagram of the coaster when it is at that point. There will be the weight of the coaster acting vertically down equal to [tex] mg[/tex], and a Normal force, N, acting on the coaster from the tracks, which might be up, down, or nothing at all. The problem statement implies that N is 0, since it states that only gravity can be counted on to supply the force necessary to keep the coaster from flying off the tracks. So therefore, only gravity is considered acting, and you apply the centripetal force equation to detrmine the speed v_A.. The centripetal force equation for motion in a circle is
[tex]F_{net} = mv^2/R[/tex], where R is the radius of the circle, v is the speed of the object tangent to the circle, and F_{net} always points toward the center of the circle (it is a centripetal or 'center-seeking' force. Please memorize this equation. Now since we have established that F_{net} = mg, and R = 25, solve for
ther unknown v_A (the mass term cancels out). Then go back and do to the Conservation of Energy thing.
 
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FAQ: What is the Kinetic Energy at Point A?

What is the "Rollercoaster of Physics"?

The "Rollercoaster of Physics" is a term used to describe the application of physics principles to the design and operation of rollercoasters.

How do physics principles play a role in rollercoaster design?

Physics principles such as gravity, energy, and forces are essential in determining the speed, height, and overall safety of a rollercoaster. The design of a rollercoaster must take into account these principles to ensure a thrilling yet safe ride for passengers.

What are some specific examples of physics principles used in rollercoaster design?

Some specific examples of physics principles used in rollercoaster design include the conservation of energy, centripetal force, and friction. These principles help determine the height of the first drop, the shape of the track, and the speed of the ride.

What are some safety measures taken in rollercoaster design to prevent accidents?

Rollercoaster designers use physics principles to ensure the safety of passengers. For example, the track is designed to provide enough centripetal force to keep the cars on the track and prevent them from flying off. Additionally, safety restraints and emergency braking systems are also incorporated into rollercoaster design.

Are there any advancements in rollercoaster design made possible by physics?

Yes, advancements in technology and understanding of physics have led to more innovative and thrilling rollercoaster designs. For example, the use of magnetic propulsion systems and virtual reality technology have enhanced the rollercoaster experience while also ensuring the safety of passengers.

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