Does a Roller Coaster Conserve Mechanical Energy?

[Jabababa]

Homework Statement

1.What is the highest potential energy?

2.What is the biggest change in kinetic energy?

3.If the track is only designed to uses electricity to pull the cars up the first incline, does the rollercoaster experience conservation of mechanical energy? Explain your answer.

Homework Equations

The Attempt at a Solution

1. highest potential energy would be at the start, point A where there is no movement
2. Biggest change in kinetic energy is the steepest hill, point d, mgh=1/2mv^2
3. This one i have no clue how to explain, I am kind of confused.

Please help me with #3 and explain it to me please!

 

[majormaaz]

3. I believe that the roller coaster does experience a conservation of mechanical energy. The electricity's 'energy' is channeled to push the roller coaster aka potential energy. If you think about it, we do have electrical power, but we're using it to create a change in potential energy, which is what the formula says: Delta U = Delta K.
Just as future reference, you violate the conservation of energy 'law' only when an energy term like friction or air resistance is in the equation - forces that affect only one direction of movement, and not the opposite direction

 

[Jabababa]

Thank you for helping out, majormaaz. So the way you explained it is electricity is just to help the roller coaster get to the top of the 1st hill and the eletricity does not actually add in any kind of energy, Ek + Ep = Ek + Ep + Eneregy...

And for question 1, it is a multiple choice question there are options A,D,G,K. Then should D be the place with highest potential energy since it is the highest hill?

And is point D and E the place that experience the highest change in kinetic energery?

 

[CWatters]

1. highest potential energy would be at the start, point A where there is no movement

Thats not a great/best answer in my opinion. Normally they only stop where the passengers get on (although a few stop briefly at other points). Once the passengers are on most modern roller coasters pull the carriage up a ramp to a higher/highest point (the first hill as you put it.). I would answer...

"The carriage has the highest potential energy when it is at the highest point of the roller coaster".

So the way you explained it is electricity is just to help the roller coaster get to the top of the 1st hill and the eletricity does not actually add in any kind of energy

Electricity is used to pull it up that first hill. So the electricity is increasing the PE. It also increases KE because it's stationary when the passengers get on (KE=0) and it doesn't usually come to a complete stop (KE>0) at the top of the first hill. At least one ride I've been on actually accelerates you all the way up the first hill.

 

[majormaaz]

And for question 1, it is a multiple choice question there are options A,D,G,K. Then should D be the place with highest potential energy since it is the highest hill?

Yes. If you take a look at the formula U = mgΔh, the Δh is the height, so the first hill, aka D, has the highest potential energy. And here's a reality check: It takes electrical energy to get up the first hill b/c you have to go against frictional energy. But once you reach the top, over the course of that first decline, your potential energy converts into kinetic energy. As you go over each consecutive, but smaller hill, your speed will decrease. Why? Because mechanical energy is constant, right? If you use some energy as potential energy for a smaller hill, you'll have the remainder for kinetic energy.
That is, if friction was made illegal on roller coasters. But I hope you get the jist of it.

 

[Riemann Metric]

Electricity is used to pull it up that first hill. So the electricity is increasing the PE. It also increases KE because it's stationary when the passengers get on (KE=0) and it doesn't usually come to a complete stop (KE>0) at the top of the first hill. At least one ride I've been on actually accelerates you all the way up the first hill.

Simply put, electrical energy is converted into mechanical energy and potential energy through the motion of pulling the coaster up to the first hill, or to accelerate it through the first segment. Keep in mind that the only point KE=0 is when the passengers are getting in, for even at the top of the highest hill, KE is needed to start it moving in the first place. Also, mechanical energy is not conserved, and neither is the electrical energy you put in, because of the nonconservative force of friction. Every moment the coaster is in contact with the tracks (so basically, at all times) and is moving, energy is lost to friction between the wheels and tracks and air resistance. The only 100% conservative force is gravity, because even the electrical energy in the wires faces some resistance (unless, of course, you are using superconductors, which have virtually zero electrical resistance).